We uncover the virtual monopoles underlying the nontrivial phases of the one-dimensional nonlinear excitations of rogue waves by extending the Dirac magnetic monopole theory to a complex plane. We find that the densit...We uncover the virtual monopoles underlying the nontrivial phases of the one-dimensional nonlinear excitations of rogue waves by extending the Dirac magnetic monopole theory to a complex plane. We find that the density zeros of the nonlinear waves on the extended complex plane constitute the virtual monopole fields with a quantized flux of elementary π. We then explain the exotic properties of rogue waves by means of a virtual monopole collision mechanism and find that the maximum amplitude amplification ratio and multiple phase steps of the high-order rogue waves are closely related to the number of their contained monopoles. These results open a new avenue for studying topological properties of nonlinear waves and provide an alternative way to understand their dynamics.展开更多
This paper employs the high-order-spectral-computational fluid dynamics(HOS-CFD)method to analyze the motion responses of a moored container ship at three positions in a rogue wave:before,at,and after its maximum wave...This paper employs the high-order-spectral-computational fluid dynamics(HOS-CFD)method to analyze the motion responses of a moored container ship at three positions in a rogue wave:before,at,and after its maximum wave height.These three positions display during the nonlinear evolution of the rogue wave.Numerical results are validated against physical wave tank experiments,where the rogue wave is accurately reproduced using the HOS method.The numerical results of position-dependent hydrodynamic responses in the rogue wave show that the maximum heave and surge motions do not occur at the location of maximum wave height.The heave motion peak appears before the location,the surge motion peak happens afterward and the pitch motion peak is at the location.Wavelet transform analysis is adopted to explain this situation.Scattering wave field analyses are carried out to show the different scattering wave types around the ship during the evolution of the rogue wave.展开更多
To the nonlinear Schrodinger–Boussinesq system,with the aid of Adler–Moser polynomials we predict the patterns of higher-order rogue wave solutions containing multiple large parameters.The new interesting rogue wave...To the nonlinear Schrodinger–Boussinesq system,with the aid of Adler–Moser polynomials we predict the patterns of higher-order rogue wave solutions containing multiple large parameters.The new interesting rogue wave patterns of a number of true and predicted solutions are graphically illustrated,including fan-,heart-shaped structures and their skewed versions.The results are significant for both experimental and theoretical studies of rogue wave patterns of integrable systems.展开更多
In this paper,the nonlinearization of the Lax pair and the Darboux transformation method are used to construct the rogue wave on the elliptic function background in the reduced Maxwell–Bloch system,which is described...In this paper,the nonlinearization of the Lax pair and the Darboux transformation method are used to construct the rogue wave on the elliptic function background in the reduced Maxwell–Bloch system,which is described by four component nonlinear evolution equations(NLEEs).On the background of the Jacobian elliptic function,we obtain the admissible eigenvalues and the corresponding non-periodic eigenfunctions of the model spectrum problem.Then,with the help of the one-fold Darboux transformation and two-fold Darboux transformation,rogue waves on a dn-periodic background and cn-periodic background are derived,respectively.Finally,the corresponding complex dynamical properties and evolutions of the four components are illustrated graphically by choosing suitable parameters.展开更多
A compact Grammian form for N-breather solution to the complex m Kd V equation is derived using the bilinear Kadomtsev–Petviashvili hierarchy reduction method.The propagation trajectory,period,maximum points,and peak...A compact Grammian form for N-breather solution to the complex m Kd V equation is derived using the bilinear Kadomtsev–Petviashvili hierarchy reduction method.The propagation trajectory,period,maximum points,and peak value of the 1-breather solution are calculated.Additionally,through the asymptotic analysis of 2-breather solution,we show that two breathers undergo an elastic collision.By applying the generalized long-wave limit method,the fundamental and second-order rogue wave solutions for the complex m Kd V equation are obtained from the 1-breather and 2-breather solutions,respectively.We also construct the hybrid solution of a breather and a fundamental rogue wave for the complex m Kd V equation from the 2-breather solution.Furthermore,the hybrid solution of two breathers and a fundamental rogue wave as well as the hybrid solution of a breather and a second-order rogue wave for the complex m Kd V equation are derived from the 3-breather solution via the generalized long-wave limit method.By controlling the phase parameters of breathers,the diverse phenomena of interaction between the breathers and the rogue waves are demonstrated.展开更多
In this paper,by using the Darboux transformation(DT)method and the Taylor expansion method,a new nth-order determinant of the hybrid rogue waves and breathers solution on the double-periodic background of the Kundu-D...In this paper,by using the Darboux transformation(DT)method and the Taylor expansion method,a new nth-order determinant of the hybrid rogue waves and breathers solution on the double-periodic background of the Kundu-DNLS equation is constructed when n is even.Breathers and rogue waves can be obtained from this determinant,respectively.Further to this,the hybrid rogue waves and breathers solutions on the different periodic backgrounds are given explicitly,including the single-periodic background,the double-periodic background and the plane wave background by selecting different parameters.In addition,the form of the obtained solutions is summarized.展开更多
Based on the long wave limit method,the general form of the second-order and third-order rogue wave solutions to the focusing nonlinear Schr?dinger equation are given by introducing some arbitrary parameters.The inter...Based on the long wave limit method,the general form of the second-order and third-order rogue wave solutions to the focusing nonlinear Schr?dinger equation are given by introducing some arbitrary parameters.The interaction solutions between the first-order rogue wave and one-breather wave are constructed by taking a long wave limit on the two-breather solutions.By applying the same method to the three-breather solutions,two types of interaction solutions are obtained,namely the first-order rogue wave and two breather waves,the second-order rogue wave and one-breather wave,respectively.The influence of the parameters related to the phase on the interaction phenomena is graphically demonstrated.Collisions occur among the rogue waves and breather waves.After the collisions,the shape of them remains unchanged.The abundant interaction phenomena in this paper will contribute to a better understanding of the propagation and control of nonlinear waves.展开更多
In this paper, the rogue wave solutions of the(2+1)-dimensional Myrzakulov–Lakshmanan(ML)-Ⅳ equation, which is described by five component nonlinear evolution equations, are studied on a periodic background. By usin...In this paper, the rogue wave solutions of the(2+1)-dimensional Myrzakulov–Lakshmanan(ML)-Ⅳ equation, which is described by five component nonlinear evolution equations, are studied on a periodic background. By using the Jacobian elliptic function expansion method, the Darboux transformation(DT) method and the nonlinearization of the Lax pair, two kinds of rogue wave solutions which are expressed by Jacobian elliptic functions dn and cn, are obtained.The relationship between these five kinds of potential is summarized systematically. Firstly, the periodic rogue wave solution of one potential is obtained, and then the periodic rogue wave solutions of the other four potentials are obtained directly. The solutions we find present the dynamic phenomena of higher-order nonlinear wave equations.展开更多
A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics ...A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 </sub>but also has a relationship with the other parameters c<sub>0</sub>, α, β.展开更多
The optical rogue wave(RW),known as a short-lived extraordinarily high amplitude dynamics phenomenon with small appearing probabilities,plays an important role in revealing and understanding the fundamental physics of...The optical rogue wave(RW),known as a short-lived extraordinarily high amplitude dynamics phenomenon with small appearing probabilities,plays an important role in revealing and understanding the fundamental physics of nonlinear wave propagations in optical systems.The random fiber laser(RFL),featured with cavity-free and“modeless”structure,has opened up new avenues for fundamental physics research and potential practical applications combining nonlinear optics and laser physics.Here,the extreme event of optical RW induced by noise-driven modulation instability that interacts with the cascaded stimulated Brillouin scattering,the quasi-phase-matched four-wave mixing as well as the random mode resonance process is observed in a Brillouin random fiber laser comb(BRFLC).Temporal and statistical characteristics of the RWs concerning their emergence and evolution are experimentally explored and analyzed.Specifically,temporally localized structures with high intensities including chair-like pulses with a sharp leading edge followed by a trailing plateau appear frequently in the BRFLC output,which can evolve to chair-like RW pulses with adjustable pulse duration and amplitude under controlled conditions.This investigation provides a deep insight into the extreme event of RWs and paves the way for RW manipulation for its generation and elimination in RFLs through adapted laser configuration.展开更多
We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic,which is nonlinear wave alternative of the Black-Scholes model.These rogue wave solutions may be used to describe t...We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic,which is nonlinear wave alternative of the Black-Scholes model.These rogue wave solutions may be used to describe thepossible physical mechanisms for rogue wave phenomenon in financial markets and related fields.展开更多
The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas.However,due to the difficulty of solving this equation,in particu...The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas.However,due to the difficulty of solving this equation,in particular in high dimensions,lots of methods are proposed to effectively obtain different kinds of solutions,such as neural networks among others.Recently,a method where some underlying physical laws are embeded into a conventional neural network is proposed to uncover the equation’s dynamical behaviors from spatiotemporal data directly.Compared with traditional neural networks,this method can obtain remarkably accurate solution with extraordinarily less data.Meanwhile,this method also provides a better physical explanation and generalization.In this paper,based on the above method,we present an improved deep learning method to recover the soliton solutions,breather solution,and rogue wave solutions of the nonlinear Schrodinger equation.In particular,the dynamical behaviors and error analysis about the one-order and two-order rogue waves of nonlinear integrable equations are revealed by the deep neural network with physical constraints for the first time.Moreover,the effects of different numbers of initial points sampled,collocation points sampled,network layers,neurons per hidden layer on the one-order rogue wave dynamics of this equation have been considered with the help of the control variable way under the same initial and boundary conditions.Numerical experiments show that the dynamical behaviors of soliton solutions,breather solution,and rogue wave solutions of the integrable nonlinear Schrodinger equation can be well reconstructed by utilizing this physically-constrained deep learning method.展开更多
Fault detection and diagnosis(FDD) facilitates reliable operation of systems. Various approaches have been proposed for FDD like Analytical redundancy(AR), Principal component analysis(PCA), Discrete event system(DES)...Fault detection and diagnosis(FDD) facilitates reliable operation of systems. Various approaches have been proposed for FDD like Analytical redundancy(AR), Principal component analysis(PCA), Discrete event system(DES) model etc., in the literature. Performance of FDD schemes greatly depends on accuracy of the sensors which measure the system parameters.Due to various reasons like faults, communication errors etc.,sensors may occasionally miss or report erroneous values of some system parameters to FDD engine, resulting in measurement inconsistency of these parameters. Schemes like AR, PCA etc.,have mechanisms to handle measurement inconsistency, however,they are computationally heavy. DES based FDD techniques are widely used because of computational simplicity, but they cannot handle measurement inconsistency efficiently. Existing DES based schemes do not use Measurement inconsistent(MI)parameters for FDD. These parameters are not permanently unmeasurable or erroneous, so ignoring them may lead to weak diagnosis. To address this issue, we propose a Measurement inconsistent discrete event system(MIDES) framework, which uses MI parameters for FDD at the instances they are measured by the sensors. Otherwise, when they are unmeasurable or erroneously reported, the MIDES invokes an estimator diagnoser that predicts the state(s) the system is expected to be in, using the subsequent parameters measured by the other sensors. The efficacy of the proposed method is illustrated using a pumpvalve system. In addition, an MIDES based intrusion detection system has been developed for detection of rogue dynamic host configuration protocol(DHCP) server attack by mapping the attack to a fault in the DES framework.展开更多
As concluded from physical theory and laboratory experiment,it is widely accepted that nonlinearities of sea state play an important role in the formation of rogue waves;however,the sea states and corresponding nonlin...As concluded from physical theory and laboratory experiment,it is widely accepted that nonlinearities of sea state play an important role in the formation of rogue waves;however,the sea states and corresponding nonlinearities of real-world rogue wave events remain poorly understood.Three rogue waves were recorded by a directional buoy located in the East China Sea during Typhoon Trami in August 2013.This study used the WAVEWATCHⅢmodel to simulate the sea state conditions pertaining to when and where those rogue waves were observed,based on which a comprehensive and full-scale analysis was performed.From the perspectives of wind and wave fields,wave system tracking,High-Order Spectral method simulation,and some characteristic sea state parameters,we concluded that the rogue waves occurred in sea states dominated by second-order nonlinearities.Moreover,third-order modulational instabilities were suppressed in these events because of the developed or fully developed sea state determined by the typhoon wave system.The method adopted in this study can provide comprehensive and full-scale analysis of rogue waves in the real world.The case studied in this paper is not considered unique,and rules could be found and confirmed in relation to other typhoon sea states through the application of our proposed method.展开更多
In this paper, a new type （or the second type） of transformation which is used to map the variable coefficient nonlinear Schr6dinger （VCNLS） equation to the usual nonlinear Schrodinger （NLS） equation is given. A...In this paper, a new type （or the second type） of transformation which is used to map the variable coefficient nonlinear Schr6dinger （VCNLS） equation to the usual nonlinear Schrodinger （NLS） equation is given. As a special case, a new kind of nonautonomous NLS equation with a t-dependent potential is introduced. Further, by using the new transformation and making full use of the known soliton and rogue wave solutions of the usual NLS equation, the corresponding kinds of solutions of a special model of the new nonautonomous NLS equation are discussed respectively. Additionally, through using the new transformation, a new expression, i.e., the non-rational formula, of the rogue wave of a special VCNLS equation is given analytically. The main differences between the two types of transformation mentioned above are listed by three items.展开更多
We study a simplified(3+1)-dimensional model equation and construct a lump solution for the special case of z=y using the Hirota bilinear method.Then,a more general form of lump solution is constructed,which contains ...We study a simplified(3+1)-dimensional model equation and construct a lump solution for the special case of z=y using the Hirota bilinear method.Then,a more general form of lump solution is constructed,which contains more arbitrary autocephalous parameters.In addition,a lumpoff solution is also derived based on the general lump solutions and a stripe soliton.Furthermore,we figure out instanton/rogue wave solutions via introducing two stripe solitons.Finally,one can better illustrate these propagation phenomena of these solutions by analyzing images.展开更多
Based on the developed Darboux transformation, we investigate the exact asymmetric solutions of breather and rogue waves in pair-transition-coupled nonlinear Schr?dinger equations. As an example, some types of exact b...Based on the developed Darboux transformation, we investigate the exact asymmetric solutions of breather and rogue waves in pair-transition-coupled nonlinear Schr?dinger equations. As an example, some types of exact breather solutions are given analytically by adjusting the parameters. Moreover, the interesting fundamental problem is to clarify the formation mechanism of asymmetry breather solutions and how the particle number and energy exchange between the background and soliton ultimately form the breather solutions. Our results also show that the formation mechanism from breather to rogue wave arises from the transformation from the periodic total exchange into the temporal local property.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.12375005,12022513,and12235007)the National Safety Academic Fund(Grant No.U2330401)。
文摘We uncover the virtual monopoles underlying the nontrivial phases of the one-dimensional nonlinear excitations of rogue waves by extending the Dirac magnetic monopole theory to a complex plane. We find that the density zeros of the nonlinear waves on the extended complex plane constitute the virtual monopole fields with a quantized flux of elementary π. We then explain the exotic properties of rogue waves by means of a virtual monopole collision mechanism and find that the maximum amplitude amplification ratio and multiple phase steps of the high-order rogue waves are closely related to the number of their contained monopoles. These results open a new avenue for studying topological properties of nonlinear waves and provide an alternative way to understand their dynamics.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.52201372,52131102).
文摘This paper employs the high-order-spectral-computational fluid dynamics(HOS-CFD)method to analyze the motion responses of a moored container ship at three positions in a rogue wave:before,at,and after its maximum wave height.These three positions display during the nonlinear evolution of the rogue wave.Numerical results are validated against physical wave tank experiments,where the rogue wave is accurately reproduced using the HOS method.The numerical results of position-dependent hydrodynamic responses in the rogue wave show that the maximum heave and surge motions do not occur at the location of maximum wave height.The heave motion peak appears before the location,the surge motion peak happens afterward and the pitch motion peak is at the location.Wavelet transform analysis is adopted to explain this situation.Scattering wave field analyses are carried out to show the different scattering wave types around the ship during the evolution of the rogue wave.
基金supported by the National Natural Science Foundation of China(Grant Nos.11871396,12271433)Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.23JSY036)partly supported by Graduate Student Innovation Project of Northwest University(Grant No.CX2024129)。
文摘To the nonlinear Schrodinger–Boussinesq system,with the aid of Adler–Moser polynomials we predict the patterns of higher-order rogue wave solutions containing multiple large parameters.The new interesting rogue wave patterns of a number of true and predicted solutions are graphically illustrated,including fan-,heart-shaped structures and their skewed versions.The results are significant for both experimental and theoretical studies of rogue wave patterns of integrable systems.
基金supported by the National Natural Science Foundation of China(Grant No.12361052)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(Grant No.NMGIRT2414)+3 种基金the Fundamental Research Funds for the Inner Mongolia Normal University,China(Grant Nos.2022JBTD007,2022JBXC013)Graduate Students'Research and Innovation Fund of Inner Mongolia Autonomous Region(Grant No.B20231053Z)the Key Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application(Inner Mongolia Normal University),the Ministry of Education(Grant Nos.2023KFZR01,2023KFZR02)the First-Class Disciplines Project,Inner Mongolia Autonomous Region,China(Grant No.YLXKZX-NSD-001)。
文摘In this paper,the nonlinearization of the Lax pair and the Darboux transformation method are used to construct the rogue wave on the elliptic function background in the reduced Maxwell–Bloch system,which is described by four component nonlinear evolution equations(NLEEs).On the background of the Jacobian elliptic function,we obtain the admissible eigenvalues and the corresponding non-periodic eigenfunctions of the model spectrum problem.Then,with the help of the one-fold Darboux transformation and two-fold Darboux transformation,rogue waves on a dn-periodic background and cn-periodic background are derived,respectively.Finally,the corresponding complex dynamical properties and evolutions of the four components are illustrated graphically by choosing suitable parameters.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12061051 and 12461048)。
文摘A compact Grammian form for N-breather solution to the complex m Kd V equation is derived using the bilinear Kadomtsev–Petviashvili hierarchy reduction method.The propagation trajectory,period,maximum points,and peak value of the 1-breather solution are calculated.Additionally,through the asymptotic analysis of 2-breather solution,we show that two breathers undergo an elastic collision.By applying the generalized long-wave limit method,the fundamental and second-order rogue wave solutions for the complex m Kd V equation are obtained from the 1-breather and 2-breather solutions,respectively.We also construct the hybrid solution of a breather and a fundamental rogue wave for the complex m Kd V equation from the 2-breather solution.Furthermore,the hybrid solution of two breathers and a fundamental rogue wave as well as the hybrid solution of a breather and a second-order rogue wave for the complex m Kd V equation are derived from the 3-breather solution via the generalized long-wave limit method.By controlling the phase parameters of breathers,the diverse phenomena of interaction between the breathers and the rogue waves are demonstrated.
基金supported by the National Natural Science Foundation of China under(Grant No.12361052)the Natural Science Foundation of Inner Mongolia Autonomous Region China under(Grant No.2020LH01010,2022ZD05)+1 种基金Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(Grant No.NMGIRT2414)the Fundamental Research Founds for the Inner Mongolia Normal University(Grant No.2022JBTD007).
文摘In this paper,by using the Darboux transformation(DT)method and the Taylor expansion method,a new nth-order determinant of the hybrid rogue waves and breathers solution on the double-periodic background of the Kundu-DNLS equation is constructed when n is even.Breathers and rogue waves can be obtained from this determinant,respectively.Further to this,the hybrid rogue waves and breathers solutions on the different periodic backgrounds are given explicitly,including the single-periodic background,the double-periodic background and the plane wave background by selecting different parameters.In addition,the form of the obtained solutions is summarized.
基金supported by the National Natural Science Foundation of China under Grant No.12275017the Beijing Laboratory of National Economic Security Early-warning Engineering,Beijing Jiaotong University。
文摘Based on the long wave limit method,the general form of the second-order and third-order rogue wave solutions to the focusing nonlinear Schr?dinger equation are given by introducing some arbitrary parameters.The interaction solutions between the first-order rogue wave and one-breather wave are constructed by taking a long wave limit on the two-breather solutions.By applying the same method to the three-breather solutions,two types of interaction solutions are obtained,namely the first-order rogue wave and two breather waves,the second-order rogue wave and one-breather wave,respectively.The influence of the parameters related to the phase on the interaction phenomena is graphically demonstrated.Collisions occur among the rogue waves and breather waves.After the collisions,the shape of them remains unchanged.The abundant interaction phenomena in this paper will contribute to a better understanding of the propagation and control of nonlinear waves.
基金supported by the National Natural Science Foundation of China (Grant No. 12 361 052)the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant Nos. 2020LH01010, 2022ZD05)+2 种基金the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region (Grant No. NMGIRT2414)the Fundamental Research Funds for the Inner Mongolia Normal University, China (Grant No. 2022JBTD007)the Key Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application (Inner Mongolia Normal University), and the Ministry of Education (Grant Nos. 2023KFZR01, 2023KFZR02)
文摘In this paper, the rogue wave solutions of the(2+1)-dimensional Myrzakulov–Lakshmanan(ML)-Ⅳ equation, which is described by five component nonlinear evolution equations, are studied on a periodic background. By using the Jacobian elliptic function expansion method, the Darboux transformation(DT) method and the nonlinearization of the Lax pair, two kinds of rogue wave solutions which are expressed by Jacobian elliptic functions dn and cn, are obtained.The relationship between these five kinds of potential is summarized systematically. Firstly, the periodic rogue wave solution of one potential is obtained, and then the periodic rogue wave solutions of the other four potentials are obtained directly. The solutions we find present the dynamic phenomena of higher-order nonlinear wave equations.
文摘A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 </sub>but also has a relationship with the other parameters c<sub>0</sub>, α, β.
基金supported by the National Natural Science Foundation of China (Grant No.62105180)the Natural Science Foundation of Shandong Province (Grant Nos.ZR2020MF110 and ZR2020MF118)+2 种基金the Taishan Scholar Foundation of Shandong Province (Grant No.tsqn202211027)the Qilu Young Scholar Program of Shandong Universitythe National Grant Program for High-level Returning Oversea Talents (2023).
文摘The optical rogue wave(RW),known as a short-lived extraordinarily high amplitude dynamics phenomenon with small appearing probabilities,plays an important role in revealing and understanding the fundamental physics of nonlinear wave propagations in optical systems.The random fiber laser(RFL),featured with cavity-free and“modeless”structure,has opened up new avenues for fundamental physics research and potential practical applications combining nonlinear optics and laser physics.Here,the extreme event of optical RW induced by noise-driven modulation instability that interacts with the cascaded stimulated Brillouin scattering,the quasi-phase-matched four-wave mixing as well as the random mode resonance process is observed in a Brillouin random fiber laser comb(BRFLC).Temporal and statistical characteristics of the RWs concerning their emergence and evolution are experimentally explored and analyzed.Specifically,temporally localized structures with high intensities including chair-like pulses with a sharp leading edge followed by a trailing plateau appear frequently in the BRFLC output,which can evolve to chair-like RW pulses with adjustable pulse duration and amplitude under controlled conditions.This investigation provides a deep insight into the extreme event of RWs and paves the way for RW manipulation for its generation and elimination in RFLs through adapted laser configuration.
基金Supported by National Natural Science Foundation of China under Grant No.60821002/F02
文摘We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic,which is nonlinear wave alternative of the Black-Scholes model.These rogue wave solutions may be used to describe thepossible physical mechanisms for rogue wave phenomenon in financial markets and related fields.
基金supported by the National Natural Science Foundation of China (Grant No. 11675054)the Fund from Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (Grant No. ZF1213)the Project of Science and Technology Commission of Shanghai Municipality (Grant No. 18dz2271000)。
文摘The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas.However,due to the difficulty of solving this equation,in particular in high dimensions,lots of methods are proposed to effectively obtain different kinds of solutions,such as neural networks among others.Recently,a method where some underlying physical laws are embeded into a conventional neural network is proposed to uncover the equation’s dynamical behaviors from spatiotemporal data directly.Compared with traditional neural networks,this method can obtain remarkably accurate solution with extraordinarily less data.Meanwhile,this method also provides a better physical explanation and generalization.In this paper,based on the above method,we present an improved deep learning method to recover the soliton solutions,breather solution,and rogue wave solutions of the nonlinear Schrodinger equation.In particular,the dynamical behaviors and error analysis about the one-order and two-order rogue waves of nonlinear integrable equations are revealed by the deep neural network with physical constraints for the first time.Moreover,the effects of different numbers of initial points sampled,collocation points sampled,network layers,neurons per hidden layer on the one-order rogue wave dynamics of this equation have been considered with the help of the control variable way under the same initial and boundary conditions.Numerical experiments show that the dynamical behaviors of soliton solutions,breather solution,and rogue wave solutions of the integrable nonlinear Schrodinger equation can be well reconstructed by utilizing this physically-constrained deep learning method.
基金supported by TATA Consultancy Services(TCS),India through TCS Research Fellowship Program
文摘Fault detection and diagnosis(FDD) facilitates reliable operation of systems. Various approaches have been proposed for FDD like Analytical redundancy(AR), Principal component analysis(PCA), Discrete event system(DES) model etc., in the literature. Performance of FDD schemes greatly depends on accuracy of the sensors which measure the system parameters.Due to various reasons like faults, communication errors etc.,sensors may occasionally miss or report erroneous values of some system parameters to FDD engine, resulting in measurement inconsistency of these parameters. Schemes like AR, PCA etc.,have mechanisms to handle measurement inconsistency, however,they are computationally heavy. DES based FDD techniques are widely used because of computational simplicity, but they cannot handle measurement inconsistency efficiently. Existing DES based schemes do not use Measurement inconsistent(MI)parameters for FDD. These parameters are not permanently unmeasurable or erroneous, so ignoring them may lead to weak diagnosis. To address this issue, we propose a Measurement inconsistent discrete event system(MIDES) framework, which uses MI parameters for FDD at the instances they are measured by the sensors. Otherwise, when they are unmeasurable or erroneously reported, the MIDES invokes an estimator diagnoser that predicts the state(s) the system is expected to be in, using the subsequent parameters measured by the other sensors. The efficacy of the proposed method is illustrated using a pumpvalve system. In addition, an MIDES based intrusion detection system has been developed for detection of rogue dynamic host configuration protocol(DHCP) server attack by mapping the attack to a fault in the DES framework.
基金Supported by the National Key Research and Development Program of China(Nos.2016YFC1402004,2016YFC1401805)
文摘As concluded from physical theory and laboratory experiment,it is widely accepted that nonlinearities of sea state play an important role in the formation of rogue waves;however,the sea states and corresponding nonlinearities of real-world rogue wave events remain poorly understood.Three rogue waves were recorded by a directional buoy located in the East China Sea during Typhoon Trami in August 2013.This study used the WAVEWATCHⅢmodel to simulate the sea state conditions pertaining to when and where those rogue waves were observed,based on which a comprehensive and full-scale analysis was performed.From the perspectives of wind and wave fields,wave system tracking,High-Order Spectral method simulation,and some characteristic sea state parameters,we concluded that the rogue waves occurred in sea states dominated by second-order nonlinearities.Moreover,third-order modulational instabilities were suppressed in these events because of the developed or fully developed sea state determined by the typhoon wave system.The method adopted in this study can provide comprehensive and full-scale analysis of rogue waves in the real world.The case studied in this paper is not considered unique,and rules could be found and confirmed in relation to other typhoon sea states through the application of our proposed method.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10971109 and 10971211supported by Program for New Century Excellent Talents in University under Grant No.NCET-08-0515
文摘In this paper, a new type （or the second type） of transformation which is used to map the variable coefficient nonlinear Schr6dinger （VCNLS） equation to the usual nonlinear Schrodinger （NLS） equation is given. As a special case, a new kind of nonautonomous NLS equation with a t-dependent potential is introduced. Further, by using the new transformation and making full use of the known soliton and rogue wave solutions of the usual NLS equation, the corresponding kinds of solutions of a special model of the new nonautonomous NLS equation are discussed respectively. Additionally, through using the new transformation, a new expression, i.e., the non-rational formula, of the rogue wave of a special VCNLS equation is given analytically. The main differences between the two types of transformation mentioned above are listed by three items.
基金Project supported by the National Natural Science Foundation of China(Grant No.11971475)。
文摘We study a simplified(3+1)-dimensional model equation and construct a lump solution for the special case of z=y using the Hirota bilinear method.Then,a more general form of lump solution is constructed,which contains more arbitrary autocephalous parameters.In addition,a lumpoff solution is also derived based on the general lump solutions and a stripe soliton.Furthermore,we figure out instanton/rogue wave solutions via introducing two stripe solitons.Finally,one can better illustrate these propagation phenomena of these solutions by analyzing images.
基金Project supported by the National Natural Science Foundation of China(Grant No.61774001)the Natural Science Foundation of Hunan Province,China(Grant No.2017JJ2045)
文摘Based on the developed Darboux transformation, we investigate the exact asymmetric solutions of breather and rogue waves in pair-transition-coupled nonlinear Schr?dinger equations. As an example, some types of exact breather solutions are given analytically by adjusting the parameters. Moreover, the interesting fundamental problem is to clarify the formation mechanism of asymmetry breather solutions and how the particle number and energy exchange between the background and soliton ultimately form the breather solutions. Our results also show that the formation mechanism from breather to rogue wave arises from the transformation from the periodic total exchange into the temporal local property.
