Geodesic
Generation of asymptotic solitons in an integrable model of stimulated Raman scattering by periodic boundary data
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003) no. 3, pp. 366-384 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{JMAG_2003_10_3_a6,
     author = {Eugene Khruslov and Vladimir Kotlyarov},
     title = {Generation of asymptotic solitons in an integrable model of stimulated {Raman} scattering by periodic boundary data},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {366--384},
     year = {2003},
     volume = {10},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2003_10_3_a6/}
}
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Eugene Khruslov; Vladimir Kotlyarov. Generation of asymptotic solitons in an integrable model of stimulated Raman scattering by periodic boundary data. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2003) no. 3, pp. 366-384. http://geodesic.mathdoc.fr/item/JMAG_2003_10_3_a6/