Integrable Discretization of the Coupled Nonlinear Schr\"{o}dinger Equations
Exactly Solvable and Integrable Systems
2007-05-23 v1
Abstract
A discrete version of the inverse scattering method proposed by Ablowitz and Ladik is generalized to study an integrable full-discretization (discrete time and discrete space) of the coupled nonlinear Schr\"{o}dinger equations. The generalization enables one to solve the initial-value problem. Soliton solutions and conserved quantities of the full-discrete system are constructed.
Keywords
Cite
@article{arxiv.nlin/0002048,
title = {Integrable Discretization of the Coupled Nonlinear Schr\"{o}dinger Equations},
author = {Takayuki Tsuchida},
journal= {arXiv preprint arXiv:nlin/0002048},
year = {2007}
}
Comments
9 pages, LaTeX209 file, to appear in Proceedings of the XXXI Symposium on Mathematical Physics (Torun, Poland, May 1999), special issue of Reports on Mathematical Physics