We use the 1-fold Darboux transformation (DT) of an inhomogeneous nonlinear Schrdinger equation (INLSE) to construct the deformed-soliton, breather, and rogue wave solutions explicitly. Furthermore, the obtained f...We use the 1-fold Darboux transformation (DT) of an inhomogeneous nonlinear Schrdinger equation (INLSE) to construct the deformed-soliton, breather, and rogue wave solutions explicitly. Furthermore, the obtained first-order deformed rogue wave solution, which is derived from the deformed breather solution through the Taylor expansion, is different from the known rogue wave solution of the nonlinear Schrdinger equation (NLSE). The effect of inhomogeneity is fully reflected in the variable height of the deformed soliton and the curved background of the deformed breather and rogue wave. By suitably adjusting the physical parameter, we show that a desired shape of the rogue wave can be generated. In particular, the newly constructed rogue wave can be reduced to the corresponding rogue wave of the nonlinear Schrdinger equation under a suitable parametric condition.展开更多
We propose a unified theory to construct exact rogue wave solutions of the (2+1)-dimensional nonlinear Schr6dinger equation with varying coefficients. And then the dynamics of the first- and the second-order optica...We propose a unified theory to construct exact rogue wave solutions of the (2+1)-dimensional nonlinear Schr6dinger equation with varying coefficients. And then the dynamics of the first- and the second-order optical rogues are investigated. Finally, the controllability of the optical rogue propagating in inhomogeneous nonlinear waveguides is discussed. By properly choosing the distributed coefficients, we demonstrate analytically that rogue waves can be restrained or even be annihilated, or emerge periodically and sustain forever. We also figure out the center-of-mass motion of the rogue waves.展开更多
By symbolic computation and a direct method, this paper presents some exact analytical solutions of the one-dimensional generalized inhomogeneous higher-order nonlinear Schrodinger equation with variable coefficients,...By symbolic computation and a direct method, this paper presents some exact analytical solutions of the one-dimensional generalized inhomogeneous higher-order nonlinear Schrodinger equation with variable coefficients, which include bright solitons, dark solitons, combined solitary wave solutions, dromions, dispersion-managed solitons, etc. The abundant structure of these solutions are shown by some interesting figures with computer simulation.展开更多
The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the ...The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the bound-state solitons of the inhomogeneous fifth-order NLS equation with ZBCs are derived by the residue theorem and the Laurent's series for the first time.Then,by combining with the robust IST,the Riemann-Hilbert(RH)problem of the inhomogeneous fifth-order NLS equation with NZBCs is revealed.Furthermore,based on the resulting RH problem,some new rogue wave solutions of the inhomogeneous fifth-order NLS equation are found by the Darboux transformation.Finally,some corresponding graphs are given by selecting appropriate parameters to further analyze the unreported dynamic characteristics of the corresponding solutions.展开更多
In this paper,we consider the Cauchy problem of a multi-dimensional radiating gas model with nonlinear radiative inhomogeneity.Such a model gives a good approximation to the radiative Euler equations,which are a funda...In this paper,we consider the Cauchy problem of a multi-dimensional radiating gas model with nonlinear radiative inhomogeneity.Such a model gives a good approximation to the radiative Euler equations,which are a fundamental system in radiative hydrodynamics with many practical applications in astrophysical and nuclear phenomena.One of our main motivations is to attempt to explore how nonlinear radiative inhomogeneity influences the behavior of entropy solutions.Simple but different phenomena are observed on relaxation limits.On one hand,the same relaxation limit such as the hyperbolic-hyperbolic type limit is obtained,even for different scaling.On the other hand,different relaxation limits including hyperbolic-hyperbolic type and hyperbolic-parabolic type limits are obtained,even for the same scaling if different conditions are imposed on nonlinear radiative inhomogeneity.展开更多
基金the National Natural Science Foundation of China(Grant No.10971109)K.C.Wong Magna Fund in Ningbo University,China+1 种基金the Natural Science Foundation of Ningbo,China(Grant No.2011A610179)the DST,DAE-BRNS,UGC,CSIR,India
文摘We use the 1-fold Darboux transformation (DT) of an inhomogeneous nonlinear Schrdinger equation (INLSE) to construct the deformed-soliton, breather, and rogue wave solutions explicitly. Furthermore, the obtained first-order deformed rogue wave solution, which is derived from the deformed breather solution through the Taylor expansion, is different from the known rogue wave solution of the nonlinear Schrdinger equation (NLSE). The effect of inhomogeneity is fully reflected in the variable height of the deformed soliton and the curved background of the deformed breather and rogue wave. By suitably adjusting the physical parameter, we show that a desired shape of the rogue wave can be generated. In particular, the newly constructed rogue wave can be reduced to the corresponding rogue wave of the nonlinear Schrdinger equation under a suitable parametric condition.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11072219 and 11005092)
文摘We propose a unified theory to construct exact rogue wave solutions of the (2+1)-dimensional nonlinear Schr6dinger equation with varying coefficients. And then the dynamics of the first- and the second-order optical rogues are investigated. Finally, the controllability of the optical rogue propagating in inhomogeneous nonlinear waveguides is discussed. By properly choosing the distributed coefficients, we demonstrate analytically that rogue waves can be restrained or even be annihilated, or emerge periodically and sustain forever. We also figure out the center-of-mass motion of the rogue waves.
基金Project supported by the National Natural Science Foundation of China (Grant No.10735030)Natural Science Foundation of Zhejiang Province of China (Grant No.Y6090592)+1 种基金Natural Science Foundation of Ningbo City (Grant No.2008A610017)K.C.Wong Magna Fund in Ningbo University
文摘By symbolic computation and a direct method, this paper presents some exact analytical solutions of the one-dimensional generalized inhomogeneous higher-order nonlinear Schrodinger equation with variable coefficients, which include bright solitons, dark solitons, combined solitary wave solutions, dromions, dispersion-managed solitons, etc. The abundant structure of these solutions are shown by some interesting figures with computer simulation.
基金supported by the National Natural Science Foundation of China under Grant No.11975306the Natural Science Foundation of Jiangsu Province under Grant No.BK20181351+1 种基金the Six Talent Peaks Project in Jiangsu Province under Grant No.JY-059the Fundamental Research Fund for the Central Universities under the Grant Nos.2019ZDPY07 and 2019QNA35。
文摘The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the bound-state solitons of the inhomogeneous fifth-order NLS equation with ZBCs are derived by the residue theorem and the Laurent's series for the first time.Then,by combining with the robust IST,the Riemann-Hilbert(RH)problem of the inhomogeneous fifth-order NLS equation with NZBCs is revealed.Furthermore,based on the resulting RH problem,some new rogue wave solutions of the inhomogeneous fifth-order NLS equation are found by the Darboux transformation.Finally,some corresponding graphs are given by selecting appropriate parameters to further analyze the unreported dynamic characteristics of the corresponding solutions.
基金supported in part by the Natural Science Foundation of China(Nos.12171186,11771169)the grand number CCNU22QN001 of the Fundamental Research Funds for the Central Universities.
文摘In this paper,we consider the Cauchy problem of a multi-dimensional radiating gas model with nonlinear radiative inhomogeneity.Such a model gives a good approximation to the radiative Euler equations,which are a fundamental system in radiative hydrodynamics with many practical applications in astrophysical and nuclear phenomena.One of our main motivations is to attempt to explore how nonlinear radiative inhomogeneity influences the behavior of entropy solutions.Simple but different phenomena are observed on relaxation limits.On one hand,the same relaxation limit such as the hyperbolic-hyperbolic type limit is obtained,even for different scaling.On the other hand,different relaxation limits including hyperbolic-hyperbolic type and hyperbolic-parabolic type limits are obtained,even for the same scaling if different conditions are imposed on nonlinear radiative inhomogeneity.