Nagoya Mathematical Journal

Instability of periodic traveling waves for the symmetric regularized long wave equation

Jaime Angulo Pava and Carlos Alberto Banquet Brango

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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.

Article information

Source
Nagoya Math. J., Volume 219 (2015), 235-268.

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

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1445345521

Digital Object Identifier
doi:10.1215/00277630-2891870

Mathematical Reviews number (MathSciNet)
MR3413577

Zentralblatt MATH identifier
1341.35144

Subjects
Primary: 35Q51: Soliton-like equations [See also 37K40]
Secondary: 35B35: Stability 35B10: Periodic solutions 35C07: Traveling wave solutions

Keywords
linear instability nonlinear stability nonlinear instability symmetric regularized long wave equation

Citation

Angulo Pava, Jaime; Banquet Brango, Carlos Alberto. Instability of periodic traveling waves for the symmetric regularized long wave equation. Nagoya Math. J. 219 (2015), 235--268. doi:10.1215/00277630-2891870. https://projecteuclid.org/euclid.nmj/1445345521


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References

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