2024/05/18 by Jie-Fang Zhang, Zhang, Jie-Fang, Mei-Zhen Jin +3
Physics and Astronomy · Mathematics · #Nonlinear Photonic Systems #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2405.11228
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.