On Rogue wave in the Kundu-DNLS equation
Shibao Shan, Chuanzhong Li, Jingsong He
TL;DR
This paper derives explicit rogue wave solutions for the Kundu-DNLS equation using Darboux transformations and Taylor expansion, revealing various wave patterns influenced by free parameters.
Contribution
It introduces a determinant-based Darboux transformation approach to explicitly construct rogue wave solutions with multiple patterns for the Kundu-DNLS equation.
Findings
Explicit rogue wave solutions with multiple patterns are obtained.
Rogue waves are characterized by several free parameters.
The method provides a systematic way to analyze complex wave structures.
Abstract
In this paper, the determinant representation of the n-fold Darboux transformation (DT) of the Kundu-DNLS equation is given. Based on our analysis, the soliton solutions, positon solutions and breather solutions of the Kundu-DNLS equation are given explicitly. Further, we also construct the rogue wave solutions which are given by using the Taylor expansion of the breather solution. Particularly, these rogue wave solutions possess several free parameters. With the help of these parameters, these rogue waves constitute several patterns, such as fundamental pattern, triangular pattern, circular pattern.
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