Darboux transformation of the coupled nonisospectral Gross-Pitaevskii system and its multi-component generalization

被引:39
|
作者
Xu, Tao [1 ,2 ]
Chen, Yong [1 ,2 ]
机构
[1] East China Normal Univ, Shanghai Key Lab Trustworthy Comp, Shanghai 200062, Peoples R China
[2] East China Normal Univ, MOE Int Joint Lab Trustworthy Software, Shanghai 200062, Peoples R China
来源
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2018年 / 57卷
基金
中国国家自然科学基金;
关键词
Coupled Gross-Pitaevskii system; Darboux transformation; Soliton; Breather; Rogue wave; NONLINEAR SCHRODINGER-EQUATION; ROGUE WAVE SOLUTIONS; MULTI-DARK SOLITON; CONSERVATION-LAWS; MULTISOLITON; HIERARCHY;
D O I
10.1016/j.cnsns.2017.09.009
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we extend the one-component Gross-Pitaevskii (GP) equation to the two-component coupled GP system including damping term, linear and parabolic density profiles. The Lax pair with nonisospectral parameter and infinitely-many conservation laws of this coupled GP system are presented. Actually, the Darboux transformation (DT) for this kind of nonautonomous system is essentially different from the autonomous case. Consequently, we construct the DT of the coupled GP equations, besides, nonautonomous multi-solitons, one-breather and the first-order rogue wave are also obtained. Various kinds of one-soliton solution are constructed, which include stationary one-soliton and nonautonomous one-soliton propagating along the negative (positive) direction of x-axis. The interaction of two solitons and two-soliton bound state are demonstrated respectively. We get the nonautonomous one-breather on a curved background and this background is completely controlled by the parameter beta. Using a limiting process, the nonautonomous first-order rogue wave can be obtained. Furthermore, some dynamic structures of these analytical solutions are discussed in detail. In addition, the multi-component generalization of GP equations are given, then the corresponding Lax pair and DT are also constructed. (c) 2017 Elsevier B.V. All rights reserved.
引用
收藏
页码:276 / 289
页数:14
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