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

TL;DR

This paper introduces a novel analytical method to construct various two-dimensional rogue wave solutions on zero-background for the (2+1)-dimensional KdV equation, enhancing understanding of rogue wave phenomena.

Contribution

It presents a new self-mapping transformation technique to generate diverse localized rogue wave solutions in two dimensions, including line-soliton, dromion, and lump types.

Findings

Generated rogue wave solutions with exponential decay

Derived algebraically decaying rogue wave solutions

Provided a new model for two-dimensional rogue waves

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.