On the basis of analyzing the shortages of present studies on plant disease model for autonomous phenomenon, and considering the actual situation, this paper applies the joint factors of environmental change and the i...On the basis of analyzing the shortages of present studies on plant disease model for autonomous phenomenon, and considering the actual situation, this paper applies the joint factors of environmental change and the infectivity for latent plants into the system;therefore we deal with a non-autonomous plant disease model with roguing. Some sufficient conditions are established for extinction of diseases and permanence of the system in this paper.展开更多
In this study, we investigate a pine wilt transmission model with general nonlinear incidence rates and time-varying pulse roguing. Using the stroboscopic map and comparison theorem, we proved that the disease-free eq...In this study, we investigate a pine wilt transmission model with general nonlinear incidence rates and time-varying pulse roguing. Using the stroboscopic map and comparison theorem, we proved that the disease-free equilibrium is global attractive determined by the basic reproduction number <em>R</em><sub>1</sub> < 1, and in such a case, the endemic equilibrium does not exist. The disease uniformly persists only if <em>R</em><sub>2</sub> > 1.展开更多
This study employs the Smoothed Particle Hydrodynamics(SPH)method to develop a computational fluid dynamics(CFD)model for analyzing the interaction between rogue waves and mooring systems.Four floating body configurat...This study employs the Smoothed Particle Hydrodynamics(SPH)method to develop a computational fluid dynamics(CFD)model for analyzing the interaction between rogue waves and mooring systems.Four floating body configurations are investigated:(1)dual rectangular prisms,(2)rectangular prism–sphere composites,(3)sphere–rectangular prism composites,and(4)dual spheres.These configurations are systematically evaluated under varying mooring conditions to assess their hydrodynamic performance and wave attenuation capabilities.The model accurately captures the complex fluid–structure interaction dynamics between moored floating breakwaters and incident wave fields.Among the configurations,the dual rectangular prism system demonstrates superior performance in both wave dissipation and mooring force reduction.Under conditions involving dual wave makers,the influence of floating body shape and number on wave height is found to be minimal.However,dual-body arrangements consistently outperform single-body setups in terms of both energy dissipation and structural stability.From a cost-efficiency perspective,the configuration comprising two rectangular prisms connected via a single mooring system offers significant advantages in material usage and deployment feasibility.展开更多
In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reve...In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reverse space-time nonlocal Mel'nikov equation and the nonlocal twodimensional nonlinear Schr?dinger(NLS)equation.By the PINN method,we successfully derive a data-driven two soliton solution,lump solution and rogue wave solution.Numerical simulation results indicate that the error range between the data-driven solution and the exact solution is relatively small,which verifies the effectiveness of the PINN deep learning method for solving high dimensional nonlocal equations.Moreover,the parameter discovery of the partial reverse space-time nonlocal Mel'nikov equation is analysed in terms of its soliton solution for the first time.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
Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generali...Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.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 introduce a novel neural network structure called strongly constrained theory-guided neural network(SCTgNN),to investigate the behaviour of the localized solutions of the generalized nonlinear Schr?dinger(NLS)equat...We introduce a novel neural network structure called strongly constrained theory-guided neural network(SCTgNN),to investigate the behaviour of the localized solutions of the generalized nonlinear Schr?dinger(NLS)equation.This equation comprises four physically significant nonlinear evolution equations,namely,the NLS,Hirota,Lakshmanan-Porsezian-Daniel and fifth-order NLS equations.The generalized NLS equation demonstrates nonlinear effects up to quintic order,indicating rich and complex dynamics in various fields of physics.By combining concepts from the physics-informed neural network and theory-guided neural network(TgNN)models,the SCTgNN aims to enhance our understanding of complex phenomena,particularly within nonlinear systems that defy conventional patterns.To begin,we employ the TgNN method to predict the behaviour of localized waves,including solitons,rogue waves and breathers,within the generalized NLS equation.We then use the SCTgNN to predict the aforementioned localized solutions and calculate the mean square errors in both the SCTgNN and TgNN in predicting these three localized solutions.Our findings reveal that both models excel in understanding complex behaviour and provide predictions across a wide variety of situations.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
This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional ...This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.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
文摘On the basis of analyzing the shortages of present studies on plant disease model for autonomous phenomenon, and considering the actual situation, this paper applies the joint factors of environmental change and the infectivity for latent plants into the system;therefore we deal with a non-autonomous plant disease model with roguing. Some sufficient conditions are established for extinction of diseases and permanence of the system in this paper.
文摘In this study, we investigate a pine wilt transmission model with general nonlinear incidence rates and time-varying pulse roguing. Using the stroboscopic map and comparison theorem, we proved that the disease-free equilibrium is global attractive determined by the basic reproduction number <em>R</em><sub>1</sub> < 1, and in such a case, the endemic equilibrium does not exist. The disease uniformly persists only if <em>R</em><sub>2</sub> > 1.
基金funding from the National Natural Science Foundation of China(No.12462028).
文摘This study employs the Smoothed Particle Hydrodynamics(SPH)method to develop a computational fluid dynamics(CFD)model for analyzing the interaction between rogue waves and mooring systems.Four floating body configurations are investigated:(1)dual rectangular prisms,(2)rectangular prism–sphere composites,(3)sphere–rectangular prism composites,and(4)dual spheres.These configurations are systematically evaluated under varying mooring conditions to assess their hydrodynamic performance and wave attenuation capabilities.The model accurately captures the complex fluid–structure interaction dynamics between moored floating breakwaters and incident wave fields.Among the configurations,the dual rectangular prism system demonstrates superior performance in both wave dissipation and mooring force reduction.Under conditions involving dual wave makers,the influence of floating body shape and number on wave height is found to be minimal.However,dual-body arrangements consistently outperform single-body setups in terms of both energy dissipation and structural stability.From a cost-efficiency perspective,the configuration comprising two rectangular prisms connected via a single mooring system offers significant advantages in material usage and deployment feasibility.
文摘In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reverse space-time nonlocal Mel'nikov equation and the nonlocal twodimensional nonlinear Schr?dinger(NLS)equation.By the PINN method,we successfully derive a data-driven two soliton solution,lump solution and rogue wave solution.Numerical simulation results indicate that the error range between the data-driven solution and the exact solution is relatively small,which verifies the effectiveness of the PINN deep learning method for solving high dimensional nonlocal equations.Moreover,the parameter discovery of the partial reverse space-time nonlocal Mel'nikov equation is analysed in terms of its soliton solution for the first time.
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Project supported by the National Natural Science Foundation of China(Grant No.12271096)the Natural Science Foundation of Fujian Province(Grant No.2021J01302)。
文摘Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.
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the Science and Engineering Research Board,Government of India for Grant No.CRG/2021/002428DST-SERB,Government of India for providing the National Post-Doctoral Fellowship under Grant No.PDF/2023/000619+2 种基金the Department of Science and Technology (DST),India,for the financial support under the Women Scientist Scheme-Asupported by the Science and Engineering Research Board,Government of India,under Grant No.CRG/2021/002428MoE-RUSA 2.0 Physical Sciences,Government of India,for sponsoring this research work。
文摘We introduce a novel neural network structure called strongly constrained theory-guided neural network(SCTgNN),to investigate the behaviour of the localized solutions of the generalized nonlinear Schr?dinger(NLS)equation.This equation comprises four physically significant nonlinear evolution equations,namely,the NLS,Hirota,Lakshmanan-Porsezian-Daniel and fifth-order NLS equations.The generalized NLS equation demonstrates nonlinear effects up to quintic order,indicating rich and complex dynamics in various fields of physics.By combining concepts from the physics-informed neural network and theory-guided neural network(TgNN)models,the SCTgNN aims to enhance our understanding of complex phenomena,particularly within nonlinear systems that defy conventional patterns.To begin,we employ the TgNN method to predict the behaviour of localized waves,including solitons,rogue waves and breathers,within the generalized NLS equation.We then use the SCTgNN to predict the aforementioned localized solutions and calculate the mean square errors in both the SCTgNN and TgNN in predicting these three localized solutions.Our findings reveal that both models excel in understanding complex behaviour and provide predictions across a wide variety of situations.
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Project supported by the National Natural Science Foundation of China (Grant Nos.12275172 and 11905124)。
文摘This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.
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.
