%0 Journal Article
%T On an initial-boundary value problem for the nonlinear Schr    dinger equation
%A Herbert Gajewski
%J International Journal of Mathematics and Mathematical Sciences
%D 1979
%I Hindawi Publishing Corporation
%R 10.1155/s0161171279000405
%X We study an initial-boundary value problem for the nonlinear Schr    dinger 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.
%K conserved integrals
%K a priori estimates
%K unique global solution
%K convergence of Fourier's method.
%U http://dx.doi.org/10.1155/S0161171279000405