Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering

Автор(и)

  • E.A. Moskovchenko Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering National Academy of Sciences of Ukraine 47 Lenin Ave., Kharkiv, 61103, Ukraine

Ключові слова:

nonlinear equations, Riemann-Hilbert problem, the steepest descent method, asymptotics.

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 (peiwt). 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].

Mathematics Subject Classification: 37K15, 35Q15, 35B40.

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Як цитувати

(1)
Moskovchenko, E. Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering. Журн. мат. фіз. анал. геом. 2009, 5, 82-103.

Номер

Том 5 № 1 (2009)

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