A note on the stability and the bifurcation to periodic solutions for wave-hierarchy problems with dissipation (Q761073)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A note on the stability and the bifurcation to periodic solutions for wave-hierarchy problems with dissipation |
scientific article; zbMATH DE number 3887168
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the stability and the bifurcation to periodic solutions for wave-hierarchy problems with dissipation |
scientific article; zbMATH DE number 3887168 |
Statements
A note on the stability and the bifurcation to periodic solutions for wave-hierarchy problems with dissipation (English)
0 references
1984
0 references
We show that, when the equations for the wave-hierarchy problems discussed by \textit{G. B. Whitham} [Linear and nonlinear waves (1974; Zbl 0373.76001)] are augmented by a term expressing dissipation, the linearized stability condition remains unaltered. Further, we show that when the basic uniform state is unstable, it can restabilise into a quasi-steady periodic state, parametrized by the propagation speed.
0 references
equations for the wave-hierarchy problems
0 references
term expressing dissipation
0 references
linearized stability condition remains unaltered
0 references
basic uniform state is unstable
0 references
restabilise
0 references
quasi-steady periodic state
0 references
parametrized by the propagation speed
0 references
