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Elastic interaction of second-order rogue matter waves for the modified Gross–Pitaevskii equation with time-dependent trapping potential and gain/loss

Author

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  • Nkenfack, Cyrille Edgard
  • Lekeufack, Olivier Tiokeng
  • Kenmogne, Fabien
  • Yamapi, René
  • Kengne, Emmanuel

Abstract

In this work, we are interested in the one-dimensional modified Gross–Pitaevskii equation with the presence of a confining harmonic time-dependent trap and gain/loss atoms. Starting from Hirota bilinear method, we build the one- and two-soliton solutions in the context of trapping Bose–Einstein condensates. From this set, were generated various second-order rogue matter solitary waves including parabolic solitons, line-like solitons, and dromion-like structures. In addition, great emphasis was put on the influence of higher-order interactions over the amplification and stabilization processes of solitons as well as the effects of the gain/loss whose impact beyond amplification is the creation of areas of collapse and revival of solitons during propagation. Finally, we build the multi-soliton solution then making it possible to describe the elastic-type interaction processes of the various types of rogue matter waves obtained. The theoretical results obtained hence enrich the study of non-linear phenomena within Bose–Einstein condensates and more.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924013729
    DOI: 10.1016/j.chaos.2024.115820
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