A discretization of the matrix nonlinear Schrödinger equation. (English) Zbl 0970.39016

Ding, Qing

J. Phys. A, Math. Gen. 33, No. 38, 6769-6778 (2000).

From the author’s abstract: We show that a class of solutions to the discrete coupled matrix nonlinear Schrödinger equation (DCMNLSE) is gauge equivalent to the discrete equation of the Schrödinger flow of maps into the Grassmannian and the realizing gauge transformation is only the discretization of a classical gauge transformation between the matrix nonlinear Schrödinger equation (MNLSE) and the Schrödinger flow of maps into the Grassmannian. In other words, from the viewpoint of gauge equivalence, a class of solutions to the DCMNLSE is a correct discretization of the MNLSE.

Reviewer: B.G.Pachpatte (Aurangabad)

MSC:

39A12	Discrete version of topics in analysis
35Q55	NLS equations (nonlinear Schrödinger equations)
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)

Keywords:

matrix nonlinear Schrödinger equation; Schrödinger flow of maps; Grassmannian; gauge transformation; gauge equivalence; correct discretization