Darboux Transformations, Higher-Order Rational Solitons and Rogue Wave Solutions for a(2+1)-Dimensional Nonlinear Schrdinger Equation

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英文篇名：Darboux Transformations, Higher-Order Rational Solitons and Rogue Wave Solutions for a(2+1)-Dimensional Nonlinear Schrdinger Equation 作者：陈觅 ; 李彪 ; 于亚璇 英文作者：Mi Chen;Biao Li;Ya-Xuan Yu;Department of Mathematics, and Ningbo Collaborative Innovation Center of Nonlinear Harzard System of Ocean and Atmosphere, Ningbo University; 英文关键词：Darboux transformations;;nonlinear Schrdinger equation;;higher-order rational solution;;rogue wave solution 中文刊名：CITP 英文刊名：理论物理(英文版) 机构：Department of Mathematics, and Ningbo Collaborative Innovation Center of Nonlinear Harzard System of Ocean and Atmosphere, Ningbo University; 出版日期：2019-01-01 出版单位：Communications in Theoretical Physics 年：2019 期：v.71 基金：Supported by National Natural Science Foundation of China under Grant Nos.11775121 and 11435005;; K.C.Wong Magna Fund in Ningbo University 语种：英文; 页：CITP201901004 页数：10 CN：01 ISSN：11-2592/O3 分类号：31-40

摘要

By Taylor expansion of Darboux matrix, a new generalized Darboux transformations(DTs) for a(2 + 1)-dimensional nonlinear Schrdinger(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.
        By Taylor expansion of Darboux matrix, a new generalized Darboux transformations(DTs) for a(2 + 1)-dimensional nonlinear Schrdinger(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.

引文

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