Mixed problem for a nonlinear system of equations of Schrödinger type
type: Item
instance of: scholarly article
title: Mixed problem for a nonlinear system of equations of Schrödinger type
zbMATH Open document ID: 0626.35051
DOI: 10.1007/BF00966146
author: F. Ivanauskas
published in: Lithuanian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The author investigates an initial-boundary value problem for three partial differential equations describing three-particle interaction of electromagnetic waves in a nonlinear medium for the planar case. This system can be written in the form \[ \partial u/\partial t=A(\partial u/\partial x)+B(\partial^ 2u/\partial x^ 2)+C(u) \] for (x,t)\(\in (0,1)\times (0,T)\). A and B are diagonal matrices, and C is a special nonlinear function of u. It is established that under proper initial and boundary conditions a unique solution exists in suitable function spaces.
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 78A35
zbMATH DE Number: 4017479
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: initial-boundary value problem
zbMATH Keywords: three-particle interaction
zbMATH Keywords: electromagnetic waves
zbMATH Keywords: nonlinear medium
MaRDI profile type: Publication
cites work: Q4075894
cites work: Stability theory of difference schemes and iterative methods
cites work: Q5817687
full work available at URL: https://doi.org/10.1007/bf00966146
OpenAlex ID: W2008636909
description: scientific article; zbMATH DE number 4017479