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Type: Artigo de periódico
Title: Nonlinear Stability Of Periodic Traveling Wave Solutions To The Schrödinger And The Modified Korteweg-de Vries Equations
Author: Angulo Pava J.
Abstract: This work is concerned with stability properties of periodic traveling waves solutions of the focusing Schrödinger equationi ut + ux x + | u |2 u = 0 posed in R, and the modified Korteweg-de Vries equationut + 3 u2 ux + ux x x = 0 posed in R. Our principal goal in this paper is the study of positive periodic wave solutions of the equation φ{symbol}ω″ + φ{symbol}ω3 - ω φ{symbol}ω = 0, called dnoidal waves. A proof of the existence of a smooth curve of solutions with a fixed fundamental period L, ω ∈ (2 π2 / L2, + ∞) → φ{symbol}ω ∈ Hper∞ ([0, L]), is given. It is also shown that these solutions are nonlinearly stable in the energy space Hper1 ([0, L]) and unstable by perturbations with period 2L in the case of the Schrödinger equation. © 2007 Elsevier Inc. All rights reserved.
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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