ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
Proceeding cover
proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2021): 1.024
Some remarks on the stability and instability properties of solitary waves for the double dispersion equation; pp. 263–269
PDF | doi: 10.3176/proc.2015.3.09

Authors
Hüsnü Ata Erbay, Saadet Erbay, Albert Erkip
Abstract

 

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 ³ 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.

 

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