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

Symmetry Integrability and Geometry-Methods and Applications

article

Rustem R. Aydagulov¹  Alexander A. Minakov² 

[1] Lomonosov State University;A.A. Blagonravov Institute of Mechanical Engineering, Russian Academy of Sciences

关键词: stimulated Raman scattering;    Riemann–Hilbert problem;    Whitham modulation theory;    integrable systems;   

DOI  :  10.3842/SIGMA.2018.119

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown