Integrable semi-discretization of the coupled nonlinear Schrödinger equations

Details Integrable semi-discretization of the coupled nonlinear Schrödinger equations Integrable semi-discretization of the coupled nonlinear Schrödinger equations

1999-03-18

arxiv.org/abs/solv-int/9903013v1

J. Phys. A: Math. Gen. 32 (1999) 2239-2262

Nonlinear Sciences

Exactly Solvable and Integrable Systems

27 pages, LaTeX2e (IOP style)

Scientific paper

10.1088/0305-4470/32/11/016

A system of semi-discrete coupled nonlinear Schr\"{o}dinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the single-component discrete nonlinear Schr\"{o}dinger equation proposed by Ablowitz and Ladik. By means of the extension, the initial-value problem of the model is solved. Further, the integrals of motion and the soliton solutions are constructed within the framework of the extension of the inverse scattering method.

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