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Controlling second-order rogue matter wave and line bright soliton dynamics in 2D Bose–Einstein Condensate with higher-order interactions and gain/loss atoms

Author

Listed:
  • Nkenfack, Cyrille Edgard
  • Lekeufack, Olivier Tiokeng
  • Sabari, Subramaniyan
  • Yamapi, Rene
  • Kofane, Timoleon Crepin

Abstract

We investigate the two-dimensional modified Gross–Pitaevskii equation, accounting for the effects of atom gain/loss and a time-independent isotropic confining potential, utilizing the Hirota’s bilinear method. Through an appropriate bilinear form, we derive exact one-soliton and multi-soliton solutions. These solutions showcase two prominent phenomena: the second-order rogue matter wave with spatio-temporal localization, and the line soliton with double spatial localization. We demonstrate the feasibility of controlling the soliton amplitude and the effects of gain/loss resulting in areas of collapse by suitably tuning the coefficient of higher-order interactions in the Bose–Einstein condensate. Additionally, by exploring the interaction dynamics of the multi-soliton solutions, we identify elastic-type interactions, claiming the intrinsic properties of solitons. The influence of higher-order interactions and gain/loss terms on the interaction dynamics is also thoroughly analyzed. These analyses demonstrate that, within the framework of Bose–Einstein condensates described by the two-dimensional modified Gross–Pitaevskii equation, higher-order interactions provide a means to control the properties of the generated rogue matter waves. Intensive numerical simulations are performed and their convergence with theoretical predicted results then throw light about the emergent features of the chosen solutions. The exact analytical solutions derived in this study rigorously satisfy the original equation, which ensures their consistency with the numerical results and confirms their accuracy. Thus, our findings hold promise for potential future applications.

Suggested Citation

  • Nkenfack, Cyrille Edgard & Lekeufack, Olivier Tiokeng & Sabari, Subramaniyan & Yamapi, Rene & Kofane, Timoleon Crepin, 2025. "Controlling second-order rogue matter wave and line bright soliton dynamics in 2D Bose–Einstein Condensate with higher-order interactions and gain/loss atoms," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:chsofr:v:198:y:2025:i:c:s0960077925005478
    DOI: 10.1016/j.chaos.2025.116534
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    References listed on IDEAS

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    1. Jena, Rajarama Mohan & Chakraverty, Snehashish & Baleanu, Dumitru, 2020. "A novel analytical technique for the solution of time-fractional Ivancevic option pricing model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    2. Nkenfack, Cyrille Edgard & Lekeufack, Olivier Tiokeng & Kenmogne, Fabien & Yamapi, René & Kengne, Emmanuel, 2025. "Elastic interaction of second-order rogue matter waves for the modified Gross–Pitaevskii equation with time-dependent trapping potential and gain/loss," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    3. Kevin E. Strecker & Guthrie B. Partridge & Andrew G. Truscott & Randall G. Hulet, 2002. "Formation and propagation of matter-wave soliton trains," Nature, Nature, vol. 417(6885), pages 150-153, May.
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