Derivative and higher order extensions of Davey-Stewartson equation from matrix KP hierarchy

TL;DR

This paper derives new integrable equations in (2+1) dimensions from the matrix KP hierarchy, including derivative and higher order extensions of the Davey-Stewartson equation, expanding the understanding of integrable systems.

Contribution

It introduces derivative and higher order nonlinear extensions of the Davey-Stewartson equation derived from the matrix KP hierarchy, with new Lax pairs and gauge transformations.

Findings

New integrable (2+1)-dimensional equations derived

Higher order DSE generalizes Kundu-Eckhaus equation

Significant extensions to constrained matrix KP system

Abstract

It is shown that the matrix KP hierarchy can yield new integrable equations in $(2+1)$-dimensions along with the corresponding Lax pair. For particular gauge choice this may result derivative and also a higher order nonlinear extension of the Devay-Stewartson equation (DSE),the higher order DSE being a higher dimensional generalisation of the Kundu- Eckhaus equation. Such gauge transformation is shown also to produce significant extensions to the constrained matrix KP system.