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arXiv · 2402.09980

Do Rogue Wave Exist in the Kadomtesv-Petviashivili I Equation ?

Jie-Fang Zhang·Zhao Zhang·Meng-yang Zhang·Mei-zhen Jin
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Abstract

There is considerable fundamental theoretical and applicative interest in obtaining two-dimensional rogue wave similar to one-dimensional rogue wave of the nonlinear Schr\"odinger equation. Here, we first time proposes a self-mapping transformation and analytically predict the existence of a family of novel spatio-temporal rogue wave solutions for the Kadomtesv-Petviashivili equation. We discover that these spatio-temporal rogue waves showing a strong analogy characteristics of the short-lives with rogue waves of the NLS equation. Our fingdings can also provide a solid mathematical basis for theory and application in shallow water, plasma and optics. This technique could be available to construct rogue-like waves of (2+1)-dimensional nonlinear wave models. Also, these studies could be helpful to deepen our understandings and enrich our knowledge about rogue waves.

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Jie-Fang Zhang, Zhao Zhang, Meng-yang Zhang, Mei-zhen Jin. 2024-02-15. Do Rogue Wave Exist in the Kadomtesv-Petviashivili I Equation ?. https://arxiv.org/abs/2402.09980

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