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SIGMA, 2018, Volume 14, 119, 19 pp. (Mi sigma1418)  

Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis

Rustem R. Aydagulovab, Alexander A. Minakovcd

a Lomonosov State University, Leninskie Gory 1, Moscow, Russia
b A.A. Blagonravov Institute of Mechanical Engineering, Russian Academy of Sciences, Bardina 4, Moscow, Russia
c Institut de Recherche en Mathématique et Physique (IRMP), Université catholique de Louvain (UCL), Chemin du Cyclotron 2, Louvain-La-Neuve, Belgium
d International School for Advanced Studies (SISSA), via Bonomea 265, Trieste, Italy

Abstract: An initial-boundary value problem for a model of stimulated Raman scattering was considered in [Moskovchenko E.A., Kotlyarov V.P., J. Phys. A: Math. Theor. 43 (2010), 055205, 31 pages]. The authors showed that in the long-time range $t\to+\infty$ the $x>0$, $t>0$ quarter plane is divided into 3 regions with qualitatively different asymptotic behavior of the solution: a region of a finite amplitude plane wave, a modulated elliptic wave region and a vanishing dispersive wave region. The asymptotics in the modulated elliptic region was studied under an implicit assumption of the solvability of the corresponding Whitham type equations. Here we establish the existence of these parameters, and thus justify the results by Moskovchenko and Kotlyarov.

Keywords: stimulated Raman scattering; Riemann–Hilbert problem; Whitham modulation theory; integrable systems.

DOI: https://doi.org/10.3842/SIGMA.2018.119

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ArXiv: 1805.05153
MSC: 37K15; 35Q51; 37K40
Received: May 15, 2018; in final form October 24, 2018; Published online November 7, 2018
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Citation: Rustem R. Aydagulov, Alexander A. Minakov, “Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis”, SIGMA, 14 (2018), 119, 19 pp.

Citation in format AMSBIB
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\by Rustem~R.~Aydagulov, Alexander~A.~Minakov
\paper Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis
\jour SIGMA
\yr 2018
\vol 14
\papernumber 119
\totalpages 19
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\crossref{https://doi.org/10.3842/SIGMA.2018.119}
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