Riemann-Hilbert problem, integrability and reductions

Vladimir S. Gerdjikov; Rossen I. Ivanov; Aleksander A. Stefanov

doi:10.3934/jgm.2019009

Riemann-Hilbert problem, integrability and reductions

Vladimir S. Gerdjikov, Rossen I. Ivanov, Aleksander A. Stefanov

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

The present paper is dedicated to integrable models with Mikhailov reduction groups G _R ' 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 D _h symmetries are presented.

Original language	English
Pages (from-to)	167-185
Number of pages	19
Journal	Journal of Geometric Mechanics
Volume	11
Issue number	2
DOIs	https://doi.org/10.3934/jgm.2019009
Publication status	Published - Jun 2019

Keywords

Inverse scattering
Semisimple Lie algebras
Solitons

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abstract = " The present paper is dedicated to integrable models with Mikhailov reduction groups G R ' 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 D h symmetries are presented.",

keywords = "Inverse scattering, Semisimple Lie algebras, Solitons",

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AU - Ivanov, Rossen I.

AU - Stefanov, Aleksander A.

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PY - 2019/6

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KW - Inverse scattering

KW - Semisimple Lie algebras

KW - Solitons

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Riemann-Hilbert problem, integrability and reductions

Abstract

Keywords

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