Symmetric homoclinic solutions to the periodic orbits in the Michelson system
Keywords
Differential equations, symmetric homoclinic orbits, rigorous numerical analysisAbstract
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.Downloads
Published
2006-09-01
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WILCZAK, Daniel. Symmetric homoclinic solutions to the periodic orbits in the Michelson system. Topological Methods in Nonlinear Analysis. Online. 1 September 2006. Vol. 28, no. 1, pp. 155 - 170. [Accessed 20 April 2024].
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