1212.3444 (Oleksandr Chvartatskyi et al.)

Matrix generalizations of integrable systems with Lax
integro-differential representations    [PDF]

Oleksandr Chvartatskyi, Yuriy Sydorenko

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.

View original: http://arxiv.org/abs/1212.3444