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On the breakdown of small amplitude breathers for the reversible Klein-Gordon equation

Banff International Research Station for Mathematical Innovation and Discovery

Breathers are periodic in time spatially localized solutions of evolutionary PDEs. They are known to exist for the sine-Gordon equation but are believed to be rare in other Klein-Gordon equations. Exchanging the roles of time and position, breathers can be interpreted as homoclinic solutions to a steady solution. In this talk, I will explain how to obtain an asymptotic formula for the distance between the stable and unstable manifold of the steady solution when the steady solution has weakly hyperbolic one dimensional stable and unstable manifolds. Their distance is exponentially small with respect to the amplitude of the breather and therefore classical perturbative techniques cannot be applied. This is a joint work with O. Gomide, T. Seara and C. Zeng.

Mathematics; Dynamical systems and ergodic theory; Partial differential equations

video/mp4

Author affiliation: Universitat Politècnica de Catalunya

2019-12-11

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72667

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/