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Type: Artigo de periódico
Title: Existence and stability of periodic travelling-wave solutions of the Benjamin equation
Author: Samaniego, BA
Pava, JA
Abstract: A family of steady periodic water waves in very deep fluids when the surface tension is present and satisfying the following nonlinear pseudo-differential equation u(t) + uu(x) + u(xxx) + lHu(xx) = 0, known as the Benjamin equation, is shown to exist. Here H denotes the periodic Hilbert transform and l is an element of R. By fixing a minimal period we obtain, via the implicit function theorem, an analytic curve of periodic travelling-wave solutions depending on the parameter l. Moreover, by making some changes in the abstract stability theory developed by Grillakis, Shatah, and Strauss, we prove that these travelling waves are nonlinearly stable to perturbations with the same wavelength.
Subject: dispersive equations
KdV equation
periodic travelling-waves
cnoidal waves
nonlinear stability
Country: EUA
Editor: Amer Inst Mathematical Sciences
Citation: Communications On Pure And Applied Analysis. Amer Inst Mathematical Sciences, v. 4, n. 2, n. 367, n. 388, 2005.
Rights: aberto
Identifier DOI: 10.3934/cpaa.2005.4.367
Date Issue: 2005
Appears in Collections:Unicamp - Artigos e Outros Documentos

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