Nearly integrable nonlinear equations on the half line

Details Nearly integrable nonlinear equations on the half line Nearly integrable nonlinear equations on the half line

2000-10-02

arxiv.org/abs/nlin/0010002v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTex2e, 14 pages, no figures

Scientific paper

We employ the Riemann-Hilbert problem for solution of the initial-boundary value problems for nearly integrable equations on the half line which have important applications in physics. The detailed derivation of the integrable and perturbation-induced evolutions of the spectral data are given for the two most important models, the self-induced transparency and the stimulated Raman scattering. In particular, we prove that dephasing stabilizes the spike phenomenon in the stimulated Raman scattering.

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