By Taylor expansion of Darboux matrix, a new generalized Darboux transformations(DTs) for a(2 + 1)-dimensional nonlinear Schrdinger(NLS) equation is derived, which can be reduced to two(1 + 1)-dimensional equation:a m...By Taylor expansion of Darboux matrix, a new generalized Darboux transformations(DTs) for a(2 + 1)-dimensional nonlinear Schrdinger(NLS) equation is derived, which can be reduced to two(1 + 1)-dimensional equation:a modified KdV equation and an NLS equation. With the help of symbolic computation, some higher-order rational solutions and rogue wave(RW) solutions are constructed by its(1, N-1)-fold DTs according to determinants. From the dynamic behavior of these rogue waves discussed under some selected parameters, we find that the RWs and solitons are demonstrated some interesting structures including the triangle, pentagon, heptagon profiles, etc. Furthermore, we find that the wave structure can be changed from the higher-order RWs into higher-order rational solitons by modulating the main free parameter. These results may give an explanation and prediction for the corresponding dynamical phenomena in some physically relevant systems.展开更多
With the help of the similarity transformation connected the variable-eoeicient （3＋1）-dimensionai nonlin- ear Sehroedinger equation with the standard nonlinear Schr6dinger equation, we firstly obtain first-order an...With the help of the similarity transformation connected the variable-eoeicient （3＋1）-dimensionai nonlin- ear Sehroedinger equation with the standard nonlinear Schr6dinger equation, we firstly obtain first-order and second-order rogue wave solutions. Then, we investigate the controllable behaviors of these rogue waves in the hyperbolic dispersion decreasing profile. Our results indicate that the integral relation between the accumulated time T and the reai time t is the basis to realize the control and manipulation of propagation behaviors of rogue waves, such as sustainment and restraint. We can modulate the value To to achieve the sustained and restrained spatiotemporai rogue waves. Moreover, the controllability for position of sustainment and restraint for spatiotemporai rogue waves can aiso be realized by setting different values of Xo.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos.11775121 and 11435005K.C.Wong Magna Fund in Ningbo University
文摘By Taylor expansion of Darboux matrix, a new generalized Darboux transformations(DTs) for a(2 + 1)-dimensional nonlinear Schrdinger(NLS) equation is derived, which can be reduced to two(1 + 1)-dimensional equation:a modified KdV equation and an NLS equation. With the help of symbolic computation, some higher-order rational solutions and rogue wave(RW) solutions are constructed by its(1, N-1)-fold DTs according to determinants. From the dynamic behavior of these rogue waves discussed under some selected parameters, we find that the RWs and solitons are demonstrated some interesting structures including the triangle, pentagon, heptagon profiles, etc. Furthermore, we find that the wave structure can be changed from the higher-order RWs into higher-order rational solitons by modulating the main free parameter. These results may give an explanation and prediction for the corresponding dynamical phenomena in some physically relevant systems.
基金Supported by the National Natural Science Foundation of China under Grant No.11005092the Program for Innovative Research Team of Young Teachers under Grant No.2009RC01the Scientific Research and Developed Fund under Grant No.2009FK42 of Zhejiang A&F University
文摘With the help of the similarity transformation connected the variable-eoeicient （3＋1）-dimensionai nonlin- ear Sehroedinger equation with the standard nonlinear Schr6dinger equation, we firstly obtain first-order and second-order rogue wave solutions. Then, we investigate the controllable behaviors of these rogue waves in the hyperbolic dispersion decreasing profile. Our results indicate that the integral relation between the accumulated time T and the reai time t is the basis to realize the control and manipulation of propagation behaviors of rogue waves, such as sustainment and restraint. We can modulate the value To to achieve the sustained and restrained spatiotemporai rogue waves. Moreover, the controllability for position of sustainment and restraint for spatiotemporai rogue waves can aiso be realized by setting different values of Xo.
