Moskovchenko O. The Riemann-Hilbert problem method for integration of the system of the stimulated Raman scattering

The dissertation thesis is devoted to application of a method of the Riemann-Hilbert problem for an analysis of initial boundary value problems for the nonlinear integrable equations of stimulated Raman scattering. Object of researches: nonlinear integrable on Lax equations of stimulated Raman scattering. Purpose of researches: the construction of the solution of initial boundary value problems for integrable equations of stimulated Raman scattering and studing their long-time asymptotics behavior. Methods of researches: the method of the Riemann-Hilbert problem, the steepest descent method. Theoretical and practical results: for the solutions of initial boundary value problems as the solutions of the correspondence matrix Riemann-Hilbert problems formulas are got, solvability of matrix Riemann-Hilbert problems is proved, the formulas for long-time asymptotic behavior of the solution of the corresponding initial boundary value problem in different regions of phase domain are shown. Novelty: all results are new. Degree of introduction, sphere of the use: results have theoretical character, can be used for research other initial and initial boundary value problems for the integrable on Lax partial differential equations.