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Nearly integrable nonlinear equations on the half line

E. V. Doktorov·V. S. Shchesnovich
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Abstract

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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E. V. Doktorov, V. S. Shchesnovich. 2000-10-02. Nearly integrable nonlinear equations on the half line. https://arxiv.org/abs/nlin/0010002

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