Integrable Discretization of the Coupled Nonlinear Schrödinger Equations

Details Integrable Discretization of the Coupled Nonlinear Schrödinger Equations Integrable Discretization of the Coupled Nonlinear Schrödinger Equations

2000-02-25

arxiv.org/abs/nlin/0002048v1

Rep. Math. Phys. 46 (2000) 269-278

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages, LaTeX209 file, to appear in Proceedings of the XXXI Symposium on Mathematical Physics (Torun, Poland, May 1999), spec

Scientific paper

10.1016/S0034-4877(01)80032-X

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.

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