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Linear stability analysis for periodic travelling waves of the Boussinesq equation and the Klein–Gordon–Zakharov system

Published online by Cambridge University Press:  16 May 2014

Sevdzhan Hakkaev ,
Milena Stanislavova  and
Atanas Stefanov
Sevdzhan Hakkaev
Affiliation:
Faculty of Mathematics and Informatics, Shumen University, 9712 Shumen, Bulgaria
Milena Stanislavova
Affiliation:
Department of Mathematics, University of Kansas, 1460 Jayhawk Boulevard, Lawrence, KS 66045-7523, USA, (stanis@math.ku.edu; stefanov@math.ku.edu)
Atanas Stefanov
Affiliation:
Department of Mathematics, University of Kansas, 1460 Jayhawk Boulevard, Lawrence, KS 66045-7523, USA, (stanis@math.ku.edu; stefanov@math.ku.edu)
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Abstract

The question of the linear stability of spatially periodic waves for the Boussinesq equation (in the cases p = 2, 3) and the Klein–Gordon–Zakharov system is considered. For a wide class of solutions, we completely and explicitly characterize their linear stability (instability) when the perturbations are taken with the same period T. In particular, our results allow us to completely recover the linear stability results, in the limit T → ∞, for the whole-line case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 3 , June 2014 , pp. 455 - 489
Copyright
Copyright © Royal Society of Edinburgh 2014 

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