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Hybrid structures of the rogue waves and breather-like waves for the higher-order coupled nonlinear Schrödinger equations

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  • Zhang, Xi
  • Wang, Yu-Feng
  • Yang, Sheng-Xiong

Abstract

Under investigation in this paper is the higher-order coupled nonlinear Schrödinger system, which describe the ultrashort optical pulses in nonlinear medium. Based on Lax pair, choosing nonzero seed solutions, Nth-order hybrid solutions for the higher-order coupled nonlinear Schrödinger equations are constructed via the generalized Darboux transformation. The profile and energy distribution of three kinds of hybrid structures of the rogue waves and breather-like waves were exhibited: (I) the first-order rogue waves and one breather-like waves; (II) the second-order rogue waves and two breather-like waves; (III) the third-order rogue waves and three breather-like waves. In addition, the influences of parameters for the properties of hybrid structures are discussed.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924001140
    DOI: 10.1016/j.chaos.2024.114563
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    References listed on IDEAS

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    1. Yang, Sheng-Xiong & Wang, Yu-Feng & Zhang, Xi, 2023. "Conservation laws, Darboux transformation and localized waves for the N-coupled nonautonomous Gross–Pitaevskii equations in the Bose–Einstein condensates," Chaos, Solitons & Fractals, Elsevier, vol. 169(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. 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).
    4. D. R. Solli & C. Ropers & P. Koonath & B. Jalali, 2007. "Optical rogue waves," Nature, Nature, vol. 450(7172), pages 1054-1057, December.
    5. Dong-Il Yeom & Benjamin J. Eggleton, 2007. "Rogue waves surface in light," Nature, Nature, vol. 450(7172), pages 953-954, December.
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