Dia: Dimecres, 26 de febrer de 2020
Lloc: Aula T2 (2n pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Otavio Gomide, Universidade Federal de Goiás
Títol: Small amplitude breathers for reversible Klein-Gordon equations
Resum: reathers are nontrivial time-periodic and spatially localized solutions of evolutionary Partial Differential Equations (PDE's). It is known that the sine-Gordon equation (a special case of Klein-Gordon equation) admits an explicit family of breathers. Nevertheless this kind of solution is expected to be rare in other Klein-Gordon equations. In this work, we discuss the non-existence of small amplitude breathers for reversible Klein-Gordon equations (RKG) through a rigorous analysis. Roughly speaking, we look at the RKG as an evolutionary PDE with respect to the spatial variable in such a way that the breathers becomes a homoclinic orbits to a critical point (origin). We obtain an asymptotic formula for the distance between the stable and unstable manifolds of such critical point which happens to be exponentially small with respect to the amplitude of the breather and therefore classical Melnikov Theory cannot be used. This is a joint work with M. Guardia, T. Seara and C. Zeng.
Last updated: Mon Feb 24 09:54:26 2020