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Chaos in the Kuramoto–Sivashinsky equations—a computer-assisted proof
- Source :
-
Journal of Differential Equations . Nov2003, Vol. 194 Issue 2, p433. 27p. - Publication Year :
- 2003
-
Abstract
- In this paper, we present a new technique of proving the existence of an infinite number of symmetric periodic solutions. This technique combines the covering relations method introduced by Zgliczyn´ski (J. Differential Equations 171 (2001) 173; Methods in Nonlinear Anal. 8 (1996) 169; Nonlinearity 10 (1997) 243) with fixed set iteration method described in Lamb (Reversing symmetries in dynamical systems, Ph.D. Thesis, Universiteit van Amsterdam, 1994). As an example we present a computer-assisted proof of symbolic dynamics in the Kuramoto–Sivashinsky equations. Moreover, we prove the existence of an infinite number of symmetric and an infinite number of nonsymmetric periodic solutions. [Copyright &y& Elsevier]
- Subjects :
- *SYMBOLIC dynamics
*EQUATIONS
*DIFFERENTIABLE dynamical systems
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 194
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 10804579
- Full Text :
- https://doi.org/10.1016/S0022-0396(03)00104-9