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 investigate the coupled inhomogeneous nonlinear Schrodinger equation by the covariant prolongationstructure theory, and obtain its Lax's representation. Moreover, we present the corresponding Riccati equations,...We investigate the coupled inhomogeneous nonlinear Schrodinger equation by the covariant prolongationstructure theory, and obtain its Lax's representation. Moreover, we present the corresponding Riccati equations, Backlundtransformation, and one-soliton solution.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
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Supported by Beijing Jiao-Wei Key Project KZ200810028013the Natural Science Foundation of China under Grant No. 10871135
文摘We investigate the coupled inhomogeneous nonlinear Schrodinger equation by the covariant prolongationstructure theory, and obtain its Lax's representation. Moreover, we present the corresponding Riccati equations, Backlundtransformation, and one-soliton solution.
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.