期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 57, 期 -, 页码 276-289出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2017.09.009
关键词
Coupled Gross-Pitaevskii system; Darboux transformation; Soliton; Breather; Rogue wave
类别
资金
- Global Change Research Program of China [2015CB953904]
- National Natural Science Foundation of China [11675054, 11435005]
- Natural Science Foundation of Hebei Province [A2014210140]
- Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things [ZF1213]
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.
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