International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 3, Pages 503-522
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 Herbert Gajewski. 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.
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.