International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 3, Pages 503-522
doi:10.1155/S0161171279000405
On an initial-boundary value problem for the nonlinear Schrödinger equation
Herbert Gajewski
Akademie der Wissenschaften der DDR, Zentralinstitut für Mathematik und Mechanik, Mohrenstrabe 39, Berlin DDR- 108, Germany
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.