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

Author

Listed:
  • Wu, Xi-Hu
  • Gao, Yi-Tian
  • Yu, Xin
  • Ding, Cui-Cui

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.

Suggested Citation

  • Wu, Xi-Hu & Gao, Yi-Tian & Yu, Xin & Ding, Cui-Cui, 2022. "N-fold generalized Darboux transformation and soliton interactions for a three-wave resonant interaction system in a weakly nonlinear dispersive medium," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922009651
    DOI: 10.1016/j.chaos.2022.112786
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    Cited by:

    1. Shen, Yuan & Tian, Bo & Zhou, Tian-Yu & Cheng, Chong-Dong, 2023. "Multi-pole solitons in an inhomogeneous multi-component nonlinear optical medium," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).

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