Inverse scattering method for square matrix nonlinear Schr\"odinger equation under nonvanishing boundary conditions
Exactly Solvable and Integrable Systems
2009-11-11 v2 Other Condensed Matter
Mathematical Physics
math.MP
Abstract
Matrix generalization of the inverse scattering method is developed to solve the multicomponent nonlinear Schr\"odinger equation with nonvanishing boundary conditions. It is shown that the initial value problem can be solved exactly. The multi-soliton solution is obtained from the Gel'fand--Levitan--Marchenko equation.
Keywords
Cite
@article{arxiv.nlin/0603010,
title = {Inverse scattering method for square matrix nonlinear Schr\"odinger equation under nonvanishing boundary conditions},
author = {Jun'ichi Ieda and Masaru Uchiyama and Miki Wadati},
journal= {arXiv preprint arXiv:nlin/0603010},
year = {2009}
}
Comments
25 pages, 2 figures; (v2) title changed, typos in equations corrected, sec.3.1 modified and extended