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The nonautonomous N-soliton solutions for coupled nonlinear Schrödinger equation with arbitrary time-dependent potential

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Abstract

In this paper, we investigated the coupled nonlinear Schrödinger equations with arbitrary linear time-dependent potential, which govern the soliton dynamics in quasi-one-dimensional two-component Bose–Einstein condensates. Hirota method is developed carefully for applying into this model, and we obtain the exact nonautonomous superposition (NASP) N-soliton solutions analytically. Through manipulating the time-dependent potential, the different-type NASP solitons are reported. In particular, these new soliton solutions are the superposition of dark and bright solitons, so the general bright-bright and bright-dark (or dark-bright) soliton solutions can be obtained easily. A detailed analysis for the asymptotic behavior of solitons demonstrates that the interactions of S-type two solitons and periodic-type three solitons are all elastic in each component.

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Acknowledgements

This paper is supported by the opening project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology). The opening project number is KFJJ16-06M. And it is also supported by the Research Project Supported by Shanxi Scholarship Council of China (No. 2013-043) and Innovation Project of Shanxi Postgraduate Education (No. 2016BY063).

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  1. Department of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, Shanxi, China

    Xiao-Min Wang & Ling-Ling Zhang

  2. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, China

    Xiao-Min Wang

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Wang, XM., Zhang, LL. The nonautonomous N-soliton solutions for coupled nonlinear Schrödinger equation with arbitrary time-dependent potential. Nonlinear Dyn 88, 2291–2302 (2017). https://doi.org/10.1007/s11071-017-3377-5

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