Perturbation theory for nearly integrable multi-component nonlinear PDEs
可精确求解与可积系统
2015-06-26 v2
摘要
The Riemann-Hilbert problem associated with the integrable PDE is used as a nonlinear transformation of the nearly integrable PDE to the spectral space. The temporal evolution of the spectral data is derived with account for arbitrary perturbations and is given in the form of exact equations, which generate the sequence of approximate ODEs in successive orders with respect to the perturbation. For vector nearly integrable PDEs, embracing the vector NLS and complex modified KdV equations, the main result is formulated in a theorem. For a single vector soliton the evolution equations for the soliton parameters and first-order radiation are given in explicit form
引用
@article{arxiv.nlin/0110029,
title = {Perturbation theory for nearly integrable multi-component nonlinear PDEs},
author = {V. S. Shchesnovich},
journal= {arXiv preprint arXiv:nlin/0110029},
year = {2015}
}
备注
Submitted to Journal of Mathematical Physics (References are corrected)