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Mixed localized waves in the coupled nonlinear Schrödinger equation with higher-order effects

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  • Qi, Linming
  • Liu, Lu
  • Zhao, Weiliang

Abstract

In this work, the coupled nonlinear Schrödinger equation with higher-order effects is studied with the aid of Darboux transformation and an asymptotic analysis. We report mixed localized waves, rogue wave coexisting with breathers in the system. Under certain constraints, the structures and evolutionary processes of solutions have been influenced. For example, The phase, amplitude, and propagating direction of mixed localized waves change when rogue wave collides with breathers. Moreover, the localized waves characteristics together with collision dynamic behaviors of these explicit rogue wave and breathers are exhibited graphically and discussed in detail. These novel results may be meaningful to study integrable systems better.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924002777
    DOI: 10.1016/j.chaos.2024.114725
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    References listed on IDEAS

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    1. Seadawy, Aly R. & Rizvi, Syed T.R. & Mustafa, B. & Ali, K. & Althubiti, Saeed, 2022. "Chirped periodic waves for an cubic-quintic nonlinear Schrödinger equation with self steepening and higher order nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. 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).
    3. 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).
    4. El-Nabulsi, Rami Ahmad & Anukool, Waranont, 2023. "A family of nonlinear Schrodinger equations and their solitons solutions," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Eskandar, S. & Hoseini, S.M., 2018. "Soliton solutions and eigenfunctions of linearized operator for a higher-order nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 289-294.
    6. Porsezian, K. & Kalithasan, B., 2007. "Cnoidal and solitary wave solutions of the coupled higher order nonlinear Schrödinger equation in nonlinear optics," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 188-196.
    7. Yang, Dan-Yu & Tian, Bo & Qu, Qi-Xing & Zhang, Chen-Rong & Chen, Su-Su & Wei, Cheng-Cheng, 2021. "Lax pair, conservation laws, Darboux transformation and localized waves of a variable-coefficient coupled Hirota system in an inhomogeneous optical fiber," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    8. Chen, Yi-Xiang, 2023. "Vector peregrine composites on the periodic background in spin–orbit coupled Spin-1 Bose–Einstein condensates," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    Full references (including those not matched with items on IDEAS)

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