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періодичних видань НАН України
Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering
Репозиторій DSpace/Manakin
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Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering
Посилання:
Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering / E.A. Moskovchenko // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 1. — С. 82-103. — Бібліогр.: 14 назв. — англ.
Підтримка:
The author thanks V.P. Kotlyarov and D.G. Shepelsky for helpful discussions, comments and remarks.
Дата:
2009
Переглядів:
745
Завантажень:
393
Анотація:
We consider the initial-boundary value (IBV) problem for nonlinear equations related to the integrable model of the stimulated Raman scattering in the quarter xt-plane with vanishing at infinity initial conditions and single-frequency periodic boundary data. We propose a matrix Riemann-Hilbert problem, which provides the existence of the solution of the IBV problem for all t and allows us to obtain an explicit formula for the asymptotics of the solution, using the steepest descent method for the oscillatory matrix RH problem introduced by P. Deift and X. Zhou [6].
