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

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2018
• Hauptverfasser: Aydagulov, R.R., Minakov, A.A.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2018
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/209838
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis / R.R. Aydagulov, A.A. Minakov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 36 назв. — англ.

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→+∞, 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 were 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.