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Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II

Published 27 May 2024 in math.DS, cs.NA, math.AP, and math.NA | (2405.17087v2)

Abstract: We prove the existence of infinite number of homoclinic and heteroclinic orbits to two periodic orbits for the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions and for some fixed parameter value of the system. The proof is computer assisted and it is based on a new algorithm for rigorous integration of the variational equation for a class of dissipative PDEs on the torus.

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