The hierarchy of higher order solutions of the derivative nonlinear Schr\"odinger equation

TL;DR

This paper introduces a straightforward determinant-based method to generate higher order and rogue wave solutions for the derivative nonlinear Schrödinger equation, analyzing their dynamics and structures.

Contribution

It presents a novel, simple approach to derive complex higher order solutions and rogue waves for the derivative nonlinear Schrödinger equation.

Findings

Higher order solutions are expressed in determinant form.

The method effectively captures the dynamics of rogue waves.

Structural analysis of solutions reveals new insights.

Abstract

In this paper, we provide a simple method to generate higher order position solutions and rogue wave solutions for the derivative nonlinear Schr\"odinger equation. The formulae of these higher order solutions are given in terms of determinants. The dynamics and structures of solutions generated by this method are studied.