Nearly integrable nonlinear equations on the half line
Exactly Solvable and Integrable Systems
2007-05-23 v1 Pattern Formation and Solitons
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.
Cite
@article{arxiv.nlin/0010002,
title = {Nearly integrable nonlinear equations on the half line},
author = {E. V. Doktorov and V. S. Shchesnovich},
journal= {arXiv preprint arXiv:nlin/0010002},
year = {2007}
}
Comments
LaTex2e, 14 pages, no figures