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Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger equation

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  • Li, Bang-Qing
  • Ma, Yu-Lan

Abstract

An extended generalized Darboux transformation method is proposed to construct the hybrid rogue wave and breather solutions for a classical nonlinear Schrödinger equation. Three types of hybrid wave solutions are obtained: (i) the hybrid first-order rogue wave and breather; (ii) the hybrid second-order rogue wave and first-order breather; (iii) the hybrid first-order rogue wave and second-order breather. These solutions are novel and can be used to investigate the dynamical characteristic of the hybrid rogue waves and breathers. The control and interaction based on the parameters of the hybrid wave solution are graphically demonstrated. An exact link is established between the hybrid solutions and the rogue wave solutions via setting the parameter at special value.

Suggested Citation

  • Li, Bang-Qing & Ma, Yu-Lan, 2020. "Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304288
    DOI: 10.1016/j.amc.2020.125469
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    Cited by:

    1. Li, Bang-Qing & Ma, Yu-Lan, 2022. "Interaction properties between rogue wave and breathers to the manakov system arising from stationary self-focusing electromagnetic systems," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Lou, Yu & Zhang, Yi & Ye, Rusuo & Li, Miao, 2021. "Solitons and dynamics for the integrable nonlocal pair-transition-coupled nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    3. Qi, Linming & Liu, Lu & Zhao, Weiliang, 2024. "Mixed localized waves in the coupled nonlinear Schrödinger equation with higher-order effects," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    4. Ma, Yu-Lan & Li, Bang-Qing, 2024. "Higher-order hybrid rogue wave and breather interaction dynamics for the AB system in two-layer fluids," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 489-502.
    5. Ma, Yu-Lan & Wazwaz, Abdul-Majid & Li, Bang-Qing, 2021. "A new (3+1)-dimensional Kadomtsev–Petviashvili equation and its integrability, multiple-solitons, breathers and lump waves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 505-519.
    6. Zhang, Xi & Wang, Yu-Feng & Yang, Sheng-Xiong, 2024. "Hybrid structures of the rogue waves and breather-like waves for the higher-order coupled nonlinear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    7. Suganya, S. & Srividya, B. & Prabhu, A., 2024. "Existence of localized modes in a frustrated ferromagnetic spin chain with added biquadratic interaction," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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