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Seminario / Guardia

Martedì 28 Settembre, alle ore 17.30 in SALA di RAPPRESENTANZA,

presso il Dipartimento di Matematica "Federigo Enriques", via Saldini 50,


si terrà il seguente seminario IN PRESENZA


Prof. Marcel Guardia (UPC)

Title: Breakdown of small amplitude breathers for the nonlinear Klein-Gordon equation


Abstract: Breathers are temporally periodic and spatially localized solutions of evolutionary PDEs. They are known to exist for integrable PDEs such as the sine-Gordon equation, but are believed to be rare for general nonlinear PDEs. When the spatial dimension is equal to one, exchanging the roles of time and space variables (in the so-called spatial dynamics framework), breathers can be interpreted as homoclinic solutions to steady solutions and thus arise from the intersections of the stable and unstable manifolds of the steady states. In this talk, we shall study the nonlinear Klein-Gordon equation and show that small amplitude breathers cannot exist (under certain conditions). We also construct generalized breathers, these are solutions which are periodicin time and
in space are localized up to exponentially small (with respect to the amplitude) tails.
This is a joint work with O. Gomide, T. Seara and C. Zeng.

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24 settembre 2021
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