INSTABILITY OF PERIODIC TRAVELING WAVES FOR THE SYMMETRIC REGULARIZED LONG WAVE EQUATION

Pava, Jaime Angulo; Banquet Brango, Carlos Alberto

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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

INSTABILITY OF PERIODIC TRAVELING WAVES FOR THE SYMMETRIC REGULARIZED LONG WAVE EQUATION

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Author(s):	Pava, Jaime Angulo ^[1] ; Banquet Brango, Carlos Alberto ^[2] Total Authors: 2
Affiliation:	^[1] Univ Sao Paulo, Dept Math, Inst Matemat & Estat, BR-05508090 Sao Paulo, SP - Brazil ^[2] Univ Cordoba, Dept Matemat & Estadist, Cordoba 230002 - Colombia Total Affiliations: 2
Document type:	Journal article
Source:	Nagoya Mathematical Journal; v. 219, p. 235-268, SEP 2015.
Web of Science Citations:	0
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. (AU)

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