Symmetric homoclinic solutions to the periodic orbits in the Michelson system

Daniel Wilczak

DOI: http://dx.doi.org/10.12775/TMNA.2006.025

Abstract


The Michelson system [D. Michelson, < i> Steady solutions of the Kuramoto–Sivashinsky equation< /i> , Physica D
< b> 19< /b> (1986), 89–111] $x'''+x'+0.5x^2=c^2$ for the parameter
value $c=1$ is investigated. It was proven in \cite{8}
that the system possesses two odd periodic solutions.
We shall show that there exist infinitely many homoclinic and
heteroclinic connections between them. Moreover, we shall show
that the family of homoclinic solutions contains
a countable set of odd homoclinic solutions.

Keywords


Differential equations; symmetric homoclinic orbits; rigorous numerical analysis

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