Author
Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Publication Date
2015
Publication Place
-
Estonian Academy of Sciences
Subject
Double dispersion equation, Boussinesq equation, Solitary waves, Instability by blow-up, Orbital stability, Travelling waves
Type
Document
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
2-s2.0-84939511087
Record ID
5ed74ebd-50fb-4c12-8453-3ba3408baf81
Library Location
Natural and Mathematical Sciences
Date
2015
Sample Text
In this article we give a review of our recent results on the instability and stability properties of travelling wave solutions of the double dispersion equation utt − uxx + auxxxx − buxxtt = −(|u|p−1u)xx for p > 1, a ≥ b > 0. After a brief reminder of the general class of nonlocal wave equations to which the double dispersion equation belongs, we summarize our findings for both the existence and orbital stability/instability of travelling wave solutions to the general class of nonlocal wave equations. We then state (i) the conditions under which travelling wave solutions of the double dispersion equation are unstable by blow-up and (ii) the conditions under which the travelling waves are orbitally stable. We plot the instability/stability regions in the plane defined by wave velocity and the quotient b/a for various values of p.
DOI
10.3176/proc.2015.3.09
Cilt
64
