Integrable Discretization of the Coupled Nonlinear Schrödinger Equations
arXiv:nlin/0002048 · doi:10.1016/S0034-4877(01)80032-X
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 Schrödinger equations. The generalization enables one to solve the initial-value problem. Soliton solutions and conserved quantities of the full-discrete system are constructed.
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