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September 2015 Instability of periodic traveling waves for the symmetric regularized long wave equation
Jaime Angulo Pava, Carlos Alberto Banquet Brango
Nagoya Math. J. 219: 235-268 (September 2015). DOI: 10.1215/00277630-2891870

Abstract

We prove the linear and nonlinear instability of periodic traveling wave solutions for a generalized version of the symmetric regularized long wave (SRLW) equation. Using analytic and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so the linear instability of periodic profiles is obtained. An application of this approach is made to obtain the linear/nonlinear instability of cnoidal wave solutions for the modified SRLW (mSRLW) equation. We also prove the stability of dnoidal wave solutions associated to the equation just mentioned.

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Jaime Angulo Pava. Carlos Alberto Banquet Brango. "Instability of periodic traveling waves for the symmetric regularized long wave equation." Nagoya Math. J. 219 235 - 268, September 2015. https://doi.org/10.1215/00277630-2891870

Information

Received: 28 March 2012; Revised: 30 January 2014; Accepted: 14 August 2014; Published: September 2015
First available in Project Euclid: 20 October 2015

zbMATH: 1341.35144
MathSciNet: MR3413577
Digital Object Identifier: 10.1215/00277630-2891870

Subjects:
Primary: 35Q51
Secondary: 35B10, 35B35, 35C07

Rights: Copyright © 2015 Editorial Board, Nagoya Mathematical Journal

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Vol.219 • September 2015
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