May 12, 2026
The "Nonlinear Waves and Coherent Structures Online Colloquium" is a monthly seminar that will have speakers from a diverse range of disciplines to speak on a broad range of topics connected to nonlinear waves and coherent structures. The organizers hope this series will help maintain a sense of community and provide a broad audience with access to research developments on the forefront of this field.
NWCS Colloquium
Tere M-Seara (Departament de Matemàtiques , Universitat Politècnica de Catalunya)
Title: Non existence of small breathers in Klein-Gordon equations
Abstract: Breathers are solutions of evolutionary PDEs, which are periodic in time and spa-
tially localized. They are known to exist for the sine-Gordon equation but are believed
to be rare in other Klein-Gordon equations.
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 (in an infinite dimensional space of periodic in time solutions). Thus arise from the intersections of the stable and unstable manifolds of the steady states.
In this talk, I will show some recent results where we prove that, for a wide set of Klein-Gordon equations, small breathers do not exist.
The result will be obtained through the study, using singular perturbation theory, of the stable and unstable manifolds of the steady state, as well as their distance, for which we provide an asymptotic formula.
Due to the presence of exponential small phenomena, classical perturbative techniques cannot be applied to this problem.
How to join: An email containing the zoom link and password for the seminar will be sent out by 9:30am (Eastern Time) the day of the talk. To join the email list please register here
Speakers: To see the full list of upcoming speakers and recordings of prior talks, click here
Organizers:
Stathis Charalampidis, SDSU, San Diego
Sathyanarayanan Chandramouli, UMass Amherst
Panos Kevrekidis, UMass Amherst