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Conservation laws, Darboux transformation and localized waves for the N-coupled nonautonomous Gross–Pitaevskii equations in the Bose–Einstein condensates

Author

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

Abstract

Under investigation in this paper is the N-coupled nonautonomous Gross–Pitaevskii equations, which describe the dynamics of the Bose–Einstein condensates. Based on the Lax pair, infinitely-many conservation laws and Mth-fold Darboux transformation are constructed. Three types of the nonautonomous localized waves are obtained via the Darboux transformation. The nonautonomous bound-state soliton is observed. The profile and energy distribution of the nonautonomous breather and rogue wave are shown. The influences of coefficients for the shape and position of background wave are discussed. In addition, the interactions between three types of the nonautonomous localized waves are analyzed graphically.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s096007792300173x
    DOI: 10.1016/j.chaos.2023.113272
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    References listed on IDEAS

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    1. Daoui, Abdel Kader & Messouber, Abdelouahab & Triki, Houria & Zhou, Qin & Biswas, Anjan & Liu, Wenjun & Alzahrani, Abdullah K. & Belic, Milivoj R., 2021. "Propagation of chirped periodic and localized waves with higher-order effects through optical fibers," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. 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).
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    Cited by:

    1. 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).

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