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International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 3, Pages 503-522
http://dx.doi.org/10.1155/S0161171279000405

On an initial-boundary value problem for the nonlinear Schrödinger equation

Akademie der Wissenschaften der DDR, Zentralinstitut für Mathematik und Mechanik, Mohrenstrabe 39, Berlin DDR- 108, Germany

Received 22 August 1978

Copyright © 1979 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study an initial-boundary value problem for the nonlinear Schrödinger equation, a simple mathematical model for the interaction between electromagnetic waves and a plasma layer. We prove a global existence and uniqueness theorem and establish a Galerkin method for solving numerically the problem.