N-fold generalized Darboux transformation and soliton interactions for a three-wave resonant interaction system in a weakly nonlinear dispersive medium

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

Chaos, Solitons & Fractals, 2022, vol. 165, issue P2

Abstract: In this paper, a three-wave resonant interaction system, which describes the resonant mixing of the waves in a weakly nonlinear dispersive medium, is studied. Starting from the first-order Darboux transformation, we construct an N-fold generalized Darboux transformation (GDT) in which n different spectral parameters are involved, where n and N are the positive integers, and n≤N. Utilizing the obtained N-fold GDT, we derive three types of the Y-shaped bright-dark-bright solitons. Those solitons have different characteristic lines as follows: three rays; one ray and two curves; one ray, one line and two curves. Interactions among the three kinds of Y-shaped bright-dark-bright solitons are graphically illustrated. Those interactions are shown to be elastic.

Keywords: Three-wave resonant interaction system; Weakly nonlinear dispersive medium; Generalized Darboux transformation; Y-shaped bright-dark-bright solitons; Soliton interactions (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922009651

DOI: 10.1016/j.chaos.2022.112786

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