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Binary Darboux transformation, solitons and breathers for a second-order three-wave resonant interaction system

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Abstract

In this paper, a second-order three-wave interaction system, which belongs to a three-wave resonant interaction hierarchy, is investigated. Based on a known Lax pair, we firstly derive a binary Darboux transformation and the Nth-order analytic solutions with symbolic computation, where N is a positive integer. Behaviors of the one soliton are studied, and then, multi solitons and bound-state solitons on the zero background are investigated. When we select two of the three seed solutions as 0, the Nth-order analytic solutions describe the interactions among the breathers and three kinds of the dark-bright solitons. Moreover, we explore the influence of certain parameters on the interactions among the breathers and three kinds of the dark-bright solitons. With less than two of the three seed solutions selected as 0, the breathers and bound-state breathers are derived via the Nth-order analytic solutions.

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Data Availability Statement

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

Notes

  1. The binary DT in the determinant form obtained in this paper, which enables us to obtain the dark solitons, is different from the DT in Ref. [35].

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Funding

We have expressed our sincere thanks to the Editors and Reviewers for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant No. 11772017.

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Authors and Affiliations

  1. Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    Xi-Hu Wu, Yi-Tian Gao, Xin Yu & Cui-Cui Ding

  2. Shen Yuan Honors College, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    Xi-Hu Wu

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  1. Xi-Hu Wu
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Wu, XH., Gao, YT., Yu, X. et al. Binary Darboux transformation, solitons and breathers for a second-order three-wave resonant interaction system. Nonlinear Dyn 111, 16449–16465 (2023). https://doi.org/10.1007/s11071-023-08544-1

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