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Elastic collision among higher rogue waves and multi-solitons for nonlinear model of Rossby waves

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  • Cao, Na
  • Yin, XiaoJun
  • Xu, LiYang

Abstract

Three new paradigms are established by three theorems to describe elastic collisions among second-order rogue waves and multiple solitons. We apply three paradigms to the (2+1)-dimensional KP model for Rossby waves’ amplitude, this equation can be utilized to elaborate resonance phenomenon of Rossby waves. A phenomenon which demonstrated by the three sets of diagrams of the interactions is worth deeper consideration: when second-order rogue waves encounter solitons, the solitons cross over the second-order rogue waves, instead of being absorbed, maintain their speed, shape, and propagation direction. Meanwhile the second-order rogue waves evolving independently, instead of being swallowed by solitons, even retain their original position. An important conclusion is drawn: the collision among them is elastic. These finding challenges conventional understanding of rogue wave generation.

Suggested Citation

  • Cao, Na & Yin, XiaoJun & Xu, LiYang, 2026. "Elastic collision among higher rogue waves and multi-solitons for nonlinear model of Rossby waves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 249(C), pages 323-338.
    • Handle: RePEc:eee:matcom:v:249:y:2026:i:c:p:323-338
    DOI: 10.1016/j.matcom.2026.05.017
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