Breathers and rogue waves on the double-periodic background for the reverse-space-time derivative nonlinear Schr\"odinger equation

TL;DR

This paper constructs and analyzes various complex wave solutions, including breathers and rogue waves, on periodic backgrounds for the reverse-space-time derivative nonlinear Schrödinger equation using Darboux transformations.

Contribution

It develops Darboux transformation techniques for the reverse-space-time DNLS equation and constructs higher-order rogue waves on periodic backgrounds.

Findings

Constructed periodic, breather, and rogue wave solutions.

Analyzed dynamic behaviors and new solution structures.

Extended solutions to higher-order rogue waves.

Abstract

In the present investigation, the solutions on the periodic and double-periodic background are successfully constructed by Darboux transformation using a plane wave seed solution. Firstly, the Darboux transformation for the reverse-space-time DNLS equation is constructed. Secondly, periodic solutions, breathers, double-periodic solutions, breathers on the periodic background and double-periodic background are studied. Thirdly, the higher-order rogue waves on the periodic and double-periodic background are constructed by semi-degenerate Darboux transformations. In addition, the dynamic behaviors of the solutions are plotted to show some interesting new solution structures.