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Type: Artigo de periódico
Title: Nonlinear stability of periodic traveling wave solutions to the Schrodinger and the modified Korteweg-de Vries equations
Author: Pava, JA
Abstract: This work is concerned with stability properties of periodic traveling waves solutions of the focusing Schrodinger equation iu(t) + u(xx) + vertical bar u vertical bar(2)u = 0 posed in R, and the modified Korteweg-de Vries equation u(t) + 2u(2)u(x) + u(xxx) = 0 posed in R. Our principal goal in this paper is the study of positive periodic wave solutions of the equation phi(omega)'' + phi(3)(omega) - omega phi omega = 0, called dnoidal waves. A proof of the existence of a smooth curve of solutions with a fixed fundamental period L, omega is an element of (2 pi(2)/L-2, + infinity) -> phi omega is an element of H-per(infinity) ([0, L]), is given. It is also shown that these solutions are nonlinearly stable in the energy space H-per(1) ([0, L]) and unstable by perturbations with p period 2L in the case of the Schrodinger equation. (c) 2007 Elsevier Inc. All rights reserved.
Subject: Schrodinger equation
modified Korteweg-de Vries equation
periodic traveling waves
Jacobian elliptic functions
nonlinear stability
Country: EUA
Editor: Academic Press Inc Elsevier Science
Citation: Journal Of Differential Equations. Academic Press Inc Elsevier Science, v. 235, n. 1, n. 1, n. 30, 2007.
Rights: fechado
Identifier DOI: 10.1016/j.jde.2007.01.003
Date Issue: 2007
Appears in Collections:Unicamp - Artigos e Outros Documentos

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