Nearly integrable nonlinear equations on the half line

2000/10/02 by E. V. Doktorov, Doktorov, E. V., V. S. Shchesnovich +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS) #nlin.PS #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0010002

LaTex2e, 14 pages, no figures

arxiv created 2000/10/02 · openalex publication_date 2000/10/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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