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arXiv · 2405.11228

Rogue waves excitation on zero-background in the (2+1)-dimensional KdV equation

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

An analytical method for constructing various coherent localized solutions with short-lived characteristics is proposed based on a novel self-mapping transformation of the (2+1) dimensional KdV equation. The highlight of this method is that it allows one to generate a class of basic two--dimensional rogue waves excited on zero-background for this equation, which includes the line-soliton-induced rogue wave and dromion-induced rogue wave with exponentially decaying as well as the lump-induced rogue wave with algebraically decaying in the -plane. Our finding provides a proper candidate to describe two-dimensional rogue waves and paves a feasible path for studying rogue waves.

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Jie-Fang Zhang, Mei-zhen Jin, Meng-yang Zhang. 2024-05-18. Rogue waves excitation on zero-background in the (2+1)-dimensional KdV equation. https://arxiv.org/abs/2405.11228

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