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An initial-boundary value problem for a model of stimulated Raman scatteringwas 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 withqualitatively different asymptotic behavior of the solution: a region of afinite amplitude plane wave, a modulated elliptic wave region and a vanishingdispersive wave region. The asymptotics in the modulated elliptic region wasstudied under an implicit assumption of the solvability of the correspondingWhitham type equations. Here we establish the existence of these parameters,and thus justify the results by Moskovchenko and Kotlyarov.

symmetry, integrability and geometry: methods and applications

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