Matrix generalizations of integrable systems with Lax integro-differential representations

TL;DR

This paper develops matrix generalizations of integrable systems in (2+1) dimensions, introducing Lax pairs with integro-differential operators, and extends several classical equations to matrix and higher-dimensional forms.

Contribution

It introduces novel (2+1)-dimensional matrix Lax representations for integrable systems, including generalizations of the k-cKP hierarchy and classical equations like DS, mKdV, and Chen-Lee-Liu.

Findings

Derived matrix Lax pairs with integro-differential operators.

Extended classical integrable equations to matrix and higher-dimensional forms.

Provided new integrable systems with potential applications in mathematical physics.

Abstract

We present (2+1)-dimensional generalizations of the k-constrained Kadomtsev-Petviashvili (k-cKP) hierarchy and corresponding matrix Lax representations that consist of two integro-differential operators. Additional reductions imposed on the Lax pairs lead to matrix generalizations of Davey-Stewartson systems (DS-I,DS-II,DS-III) and (2+1)-dimensional extensions of the modified Korteweg-de Vries and the Nizhnik equation. We also present an integro-differential Lax pair for a matrix version of a (2+1)-dimensional extension of the Chen-Lee-Liu equation.