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arXiv · 1902.10276

Riemann-Hilbert problem, integrability and reductions

Vladimir S. Gerdjikov·Rossen I. Ivanov·Aleksander A. Stefanov
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Abstract

The present paper is dedicated to integrable models with Mikhailov reduction groups $G_R \simeq \mathbb{D}_h.$ Their Lax representation allows us to prove, that their solution is equivalent to solving Riemann-Hilbert problems, whose contours depend on the realization of the $G_R$-action on the spectral parameter. Two new examples of Nonlinear Evolution Equations (NLEE) with $\mathbb{D}_h$ symmetries are presented.

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Vladimir S. Gerdjikov, Rossen I. Ivanov, Aleksander A. Stefanov. 2019-02-27. Riemann-Hilbert problem, integrability and reductions. https://doi.org/10.3934/jgm.2019009

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