BIFURCATIONS IN KURAMOTO-SIVASHINSKY EQUATIONS

被引：6
|
作者：
Kashchenko, S. A. [1 ,2 ]
机构：
[1] Demidov Yaroslavl State Univ, Yaroslavl, Russia
[2] Natl Res Nucl Univ MIFI, Moscow, Russia
来源：
THEORETICAL AND MATHEMATICAL PHYSICS | 2017年 / 192卷 / 01期
关键词：
bifurcation; stability; normal form; singular perturbation; dynamics; NONLINEAR STABILITY; DYNAMICAL PROPERTIES; WAVES; SYSTEMS; FILM;
D O I：
10.1134/S0040577917070029
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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.
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页码：958 / 973
页数：16
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