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arXiv · 1212.3444

Matrix generalizations of integrable systems with Lax integro-differential representations

Oleksandr Chvartatskyi·Yuriy Sydorenko
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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.

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Oleksandr Chvartatskyi, Yuriy Sydorenko. 2012-12-14. Matrix generalizations of integrable systems with Lax integro-differential representations. https://doi.org/10.1088/1742-6596%2F411%2F1%2F012010

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