Wave propagation in nonlinear media
type: Item
instance of: scholarly article
title: Wave propagation in nonlinear media
zbMATH Open document ID: 0639.35016
DOI: 10.1016/0096-3003(87)90014-2
author: G. Adomian
published in: Applied Mathematics and Computation
publication date: 1987-01-01T00:00:00Z
review text: The solution of the nonlinear partial differential equation \[ \partial \phi /\partial t+a\phi \quad m\partial \phi /\partial x=b\partial \quad n\phi /\partial x\quad n\quad for\quad t>0,\quad x>0 \] where \(m=1,2\), and \(n=2,3,4\) subject to conditions \(\phi (x,0)=f(x)\) for \(x\geq 0\) and \(\phi (0,t)=g(t)\) and \(\lim_{x\to \infty} \phi (x,t)=0\) for \(t\geq 0\) is carried constants and f(x) and g(t) given sufficiently smooth functions satisfying \(f(0)=g(0)\). (Numerical solutions have appeared previously by \textit{M. N. Oguztöreli}, \textit{E. S. Suhubi}, and \textit{K. V. Leung} [Appl. Math. Comput. 6, 309-334 (1980; Zbl 0424.65061)].) The solution given here is an analytical approximation not involving linearization or perturbation. The appendix summarizes the decomposition method for convenient references. (The book in the 4th reference should have a 1988 date).
reviewed by: G. Adomian
Mathematics Subject Classification ID: 35G30
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 4042392
zbMATH Keywords: wave propagation
zbMATH Keywords: dispersive
zbMATH Keywords: dissipative
zbMATH Keywords: Burger's equation
zbMATH Keywords: KdV equation
zbMATH Keywords: analytical approximation
zbMATH Keywords: decomposition method
MaRDI profile type: Publication
full work available at URL: 0096-3003(87)90014-2
OpenAlex ID: W2033901872
cites work: Wave propagation in dissipative or dispersive nonlinear media: A numerical approach
cites work: Inversion of nonlinear stochastic operators
cites work: The decomposition method for nonlinear dynamical systems
cites work: An investigation of the asymptotic decomposition method for nonlinear equations in physics
cites work: On the convergence region for decomposition solutions
description: scientific article; zbMATH DE number 4042392