Generation of asymptotic solitons in an integrable model of stimulated Raman scattering by periodic boundary data

Анотація

We consider an integrable model of stimulated Raman scattering. The corresponding hyperbolic partial differential equations are referred to as SRS nonlinear equations. We study the initial boundary value Goursat problem for these equations in the quarter of (x, t)-plane. The initial function vanishes at infinity while boundary data are local perturbations of a simplest periodic functions. We obtain the representation of the solution of the SRS nonlinear equations in the quarter of (x, t)-plane via functions, satisfying Marchenko integral equations, and, on this basis, we investigate the asymptotic behavior of the solution for large time. We prove that the periodic boundary data generate an unbounded train of solitons running away from the boundary.