New integrable hierarchies gauge generated from constrained KP

TL;DR

This paper derives new integrable hierarchies from constrained KP equations by exploiting gauge freedom, leading to novel systems including multicomponent and vector generalizations of known equations.

Contribution

It introduces a systematic method to generate new integrable systems from constrained KP hierarchy using residual gauge freedom, expanding the class of integrable models.

Findings

Derived hierarchies of Kundu-Eckhaus, Yajima-Oikawa, and Melnikov equations.

Generated multicomponent and vector generalizations of these systems.

Connected gauge choices to known equations like derivative NLS and Gerdjikov-Ivanov.

Abstract

Exploiting the residual gauge freedom in the formulation of constrained KP hierarchy a number of new integrable systems are derived including hierarchies of Kundu-Eckhaus equation and higher order nonlinear extensions of Yajima-Oikawa and Melnikov hierarchy. In the multicomponent case such gauge freedom generates novel multicomponent as well as vector generalisations of the above systems, while the constrained modified KP hierarchy is found to yield another set of equations like derivative NLS, Gerdjikov-Ivanov equation and chen-Lee-Liu equation depending on the gauge choice.