Author
Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Publication Date
2016-03
Publication Place
-
Elsevier
Subject
Double dispersion equation, Instability by blow-up, Orbital stability
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
1873-5215
Record ID
81dcd8b6-efc4-40e1-b7f7-2c4e97f6378b
Library Location
Natural and Mathematical Sciences
Date
2016-03
Sample Text
In this article we are concerned with the instability and stability properties of traveling wave solutions of the double dispersion equation View the MathML source for View the MathML source, View the MathML source. The main characteristic of this equation is the existence of two sources of dispersion, characterized by the terms uxxxx and uxxtt. We obtain an explicit condition in terms of a, b and p on wave velocities ensuring that traveling wave solutions of the double dispersion equation are strongly unstable by blow up. In the special case of the Boussinesq equation (b=0), our condition reduces to the one given in the literature. For the double dispersion equation, we also investigate orbital stability of traveling waves by considering the convexity of a scalar function. We provide analytical as well as numerical results on the variation of the stability region of wave velocities with a, b and p and then state explicitly the conditions under which the traveling waves are orbitally stable.
DOI
10.1016/j.na.2015.11.019
Cilt
133
