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
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
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
Analytical solutions in terms of rational-like functions are presented for a （3＋1）-dimensional nonlinear Schrodinger equation with time-varying coefficients and a harmonica potential using the similarity transforma...Analytical solutions in terms of rational-like functions are presented for a （3＋1）-dimensional nonlinear Schrodinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.展开更多
Rogue nodes broadcasting false information in beacon messages may lead to catastrophic consequences in Vehicular Ad Hoc Networks(VANETs).Previous researchers used cryptography,trust scores,or past vehicle data to dete...Rogue nodes broadcasting false information in beacon messages may lead to catastrophic consequences in Vehicular Ad Hoc Networks(VANETs).Previous researchers used cryptography,trust scores,or past vehicle data to detect rogue nodes;however,these methods suffer from high processing delay,overhead,and False–Positive Rate(FPR).We propose herein Greenshield's traffic model–based fog computing scheme called Fog–based Rogue Node Detection(F–RouND),which dynamically utilizes the On–Board Units(OBUs)of all vehicles in the region for rogue node detection.We aim to reduce the data processing delays and FPR in detecting rogue nodes at high vehicle densities.The performance of the F–RouND framework was evaluated via simulations.Results show that the F–RouND framework ensures 45%lower processing delays,12%lower overhead,and 36%lower FPR at the urban scenario than the existing rogue node detection schemes even when the number of rogue nodes increases by up to 40%in the region.展开更多
In this paper,we construct the rogue wave solutions of the sixth-order nonlinear Schrodinger equation on a background of Jacobian elliptic functions dn and cn by means of the nonlinearization of a spectral problem and...In this paper,we construct the rogue wave solutions of the sixth-order nonlinear Schrodinger equation on a background of Jacobian elliptic functions dn and cn by means of the nonlinearization of a spectral problem and Darboux transformation approach.The solutions we find present the dynamic phenomena of higher-order nonlinear wave equations.展开更多
The derivative nonlinear Schrodinger equation, which is extensively applied in plasma physics and nonlinear optics, is analytically studied by Hirota method. Space periodic solutions are determined by means of Hirota...The derivative nonlinear Schrodinger equation, which is extensively applied in plasma physics and nonlinear optics, is analytically studied by Hirota method. Space periodic solutions are determined by means of Hirota＇s bilinear formalism, and the rogue wave solution is derived as a long-wave limit of the space periodic solution.展开更多
In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule o...In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule of the rogue wave solutions up to fourth-order. These solutions have two parameters a and ;3 which denote the contribution of the higher-order terms （dispersions and nonlinear effects） included in the HONLS equation. Two localized properties, i.e., length and width of the first-order rogue wave solution are expressed by above two parameters, which show analytically a remarkable influence of higher-order terms on the rogue wave. Moreover, profiles of the higher-order rogue wave solutions demonstrate graphically a strong compression effect along t-direction given by higher-order terms.展开更多
The generalized binary Darboux transformation for the （1 ＋2）-dimensional non-isospectral KP-H equation is presented. Moreover, as a direct application, the new rogue wave solutions for the （1＋2）-dimensional non-...The generalized binary Darboux transformation for the （1 ＋2）-dimensional non-isospectral KP-H equation is presented. Moreover, as a direct application, the new rogue wave solutions for the （1＋2）-dimensional non-isospectral KP-II equation are constructed by the generalized binary Darboux transformation.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 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.
基金Project supported by the National Natural Science Foundation of China （Grant No. 10772110） and the Natural Science Foundation of Zhejiang Province, China （Grant Nos. Y606049, Y6090681, and Y6100257）.
文摘Analytical solutions in terms of rational-like functions are presented for a （3＋1）-dimensional nonlinear Schrodinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.
文摘Rogue nodes broadcasting false information in beacon messages may lead to catastrophic consequences in Vehicular Ad Hoc Networks(VANETs).Previous researchers used cryptography,trust scores,or past vehicle data to detect rogue nodes;however,these methods suffer from high processing delay,overhead,and False–Positive Rate(FPR).We propose herein Greenshield's traffic model–based fog computing scheme called Fog–based Rogue Node Detection(F–RouND),which dynamically utilizes the On–Board Units(OBUs)of all vehicles in the region for rogue node detection.We aim to reduce the data processing delays and FPR in detecting rogue nodes at high vehicle densities.The performance of the F–RouND framework was evaluated via simulations.Results show that the F–RouND framework ensures 45%lower processing delays,12%lower overhead,and 36%lower FPR at the urban scenario than the existing rogue node detection schemes even when the number of rogue nodes increases by up to 40%in the region.
基金supported by the National Natural Science Foundation of China(Grant Nos.11861050,11261037)the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.2020LH01010)the Inner Mongolia Normal University Graduate Students Research and Innovation Fund(Grant No.CXJJS21119)。
文摘In this paper,we construct the rogue wave solutions of the sixth-order nonlinear Schrodinger equation on a background of Jacobian elliptic functions dn and cn by means of the nonlinearization of a spectral problem and Darboux transformation approach.The solutions we find present the dynamic phenomena of higher-order nonlinear wave equations.
基金Supported by the Teaching Steering Committee Research Project of Higher-Learning Institutions of Ministry of Education(JZW-16-DD-15)
文摘The derivative nonlinear Schrodinger equation, which is extensively applied in plasma physics and nonlinear optics, is analytically studied by Hirota method. Space periodic solutions are determined by means of Hirota＇s bilinear formalism, and the rogue wave solution is derived as a long-wave limit of the space periodic solution.
基金Supported by the National Natural Science Foundation of China under Grant No.11271210the K.C.Wong Magna Fund in Ningbo University
文摘In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule of the rogue wave solutions up to fourth-order. These solutions have two parameters a and ;3 which denote the contribution of the higher-order terms （dispersions and nonlinear effects） included in the HONLS equation. Two localized properties, i.e., length and width of the first-order rogue wave solution are expressed by above two parameters, which show analytically a remarkable influence of higher-order terms on the rogue wave. Moreover, profiles of the higher-order rogue wave solutions demonstrate graphically a strong compression effect along t-direction given by higher-order terms.
基金Supported by the National Natural Science Foundation of China under Grant No. 11061003 and Guangxi Natural Science Foundation under Grant No. 2013GXNSFAA019001
文摘The generalized binary Darboux transformation for the （1 ＋2）-dimensional non-isospectral KP-H equation is presented. Moreover, as a direct application, the new rogue wave solutions for the （1＋2）-dimensional non-isospectral KP-II equation are constructed by the generalized binary Darboux transformation.
