New integrable systems of derivative nonlinear Schr\"{o}dinger equations with multiple components

TL;DR

This paper introduces new integrable multi-component derivative nonlinear Schrödinger equations by generalizing existing Lax pairs and applying gauge transformations, expanding the class of solvable models in nonlinear wave theory.

Contribution

It presents novel matrix-form Lax pairs and multi-component extensions of known derivative nonlinear Schrödinger equations, enhancing the integrability framework.

Findings

Derivation of new matrix Lax pairs for derivative NLS equations

Construction of multi-component integrable equations via gauge transformations

Extension of Kaup-Newell derivative NLS to multi-component form

Abstract

The Lax pair for a derivative nonlinear Schr\"{o}dinger equation proposed by Chen-Lee-Liu is generalized into matrix form. This gives new types of integrable coupled derivative nonlinear Schr\"{o}dinger equations. By virtue of a gauge transformation, a new multi-component extension of a derivative nonlinear Schr\"{o}dinger equation proposed by Kaup-Newell is also obtained.