Bifurcations in Kuramoto–Sivashinsky equations

Bifurcations in Kuramoto–Sivashinsky equations We consider the local dynamics of the classical Kuramoto–Sivashinsky equation and its generalizations and study the problem of the existence and asymptotic behavior of periodic solutions and tori. The most interesting results are obtained in the so-called infinite-dimensional critical cases. Considering these cases, we construct special nonlinear partial differential equations that play the role of normal forms and whose nonlocal dynamics thus determine the behavior of solutions of the original boundary value problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Theoretical and Mathematical Physics Springer Journals

Bifurcations in Kuramoto–Sivashinsky equations

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Publisher
Pleiades Publishing
Copyright
Copyright © 2017 by Pleiades Publishing, Ltd.
Subject
Physics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics
ISSN
0040-5779
eISSN
1573-9333
D.O.I.
10.1134/S0040577917070029
Publisher site
See Article on Publisher Site

Abstract

We consider the local dynamics of the classical Kuramoto–Sivashinsky equation and its generalizations and study the problem of the existence and asymptotic behavior of periodic solutions and tori. The most interesting results are obtained in the so-called infinite-dimensional critical cases. Considering these cases, we construct special nonlinear partial differential equations that play the role of normal forms and whose nonlocal dynamics thus determine the behavior of solutions of the original boundary value problem.

Journal

Theoretical and Mathematical PhysicsSpringer Journals

Published: Aug 15, 2017

References

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