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Some mixed soliton wave interaction patterns and stabilities for Rabi-coupled nonlocal Gross–Pitaevskii equations

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  • Li, Li
  • Yu, Fajun

Abstract

Some mixed interactions of the soliton, breather and rogue wave(RW) formations and their dynamics are studied in Rabi-coupled Bose–Einstein condensates(BECs) with spatially varying dispersion and nonlinearity. We consider the 2-component inhomogeneous Rabi-coupled Gross–Pitaevskii (GP) equations through suitable three kinds of rotational and similarity transformations. The effects of inhomogeneity and optical lattice hyperbolic potentials of the RWs are investigated with two different forms of potential strengths, and some oscillating behaviors of dark–bright solitons, RWs and breather solitons with Rabi coupling terms are shown in 2-component condensates. We demonstrate creation of some RWs coexisting with dark–bright soliton part in second component of the 2-component GP equations. We show that some mixed interactions of vector soliton, breather and RW formations by employing parabolic cylinder modulations, and find a striking feature of Rabi coupling with spatial modulation. Further, the RWs can be converted into broad based zero background RW appearing on the top of a bright soliton by introducing spatial modulation in 2-component systems. Some dynamic behaviors of the RW solutions are investigated analytically with the external potentials, and the mixed waves, interaction patterns and stabilities for Rabi-coupled nonlocal GP systems are presented with modulation instability, which can be used to calculate nonautonomous mixed wave interactions and the potential applications for the RW phenomena.

Suggested Citation

  • Li, Li & Yu, Fajun, 2025. "Some mixed soliton wave interaction patterns and stabilities for Rabi-coupled nonlocal Gross–Pitaevskii equations," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925001845
    DOI: 10.1016/j.chaos.2025.116171
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    References listed on IDEAS

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    1. Zhenya Yan, 2009. "Financial rogue waves," Papers 0911.4259, arXiv.org, revised Sep 2010.
    2. Zhang, Jin-Liang & Li, Bao-An & Wang, Ming-Liang, 2009. "The exact solutions and the relevant constraint conditions for two nonlinear Schrödinger equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 858-865.
    3. Li, Li & Yu, Fajun, 2024. "The fourth-order dispersion effect on the soliton waves and soliton stabilities for the cubic-quintic Gross–Pitaevskii equation," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    4. D. R. Solli & C. Ropers & P. Koonath & B. Jalali, 2007. "Optical rogue waves," Nature, Nature, vol. 450(7172), pages 1054-1057, December.
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