Applied Mathematics Seminar

Speaker:  Dr. Nan Lu 

Nan is our new postdoc. He is an expert on dynamical systems.

Title: Small Generalized Breathers for Klein-Gordon Equations

Abstract: Breathers are solutions to PDEs which are periodic in time and localized in space. One famous example is the family of the breathers of the sine-Gordon equation. On the one hand, as shown by Birnir-McKean-Weinstein and Denzler, these breathers are rigid in the sense that they do not persist under small perturbations to the sine-Gordon equation. On the other hand, the formal analysis by Segur-Kruskal, for the φ-4 model, which can be viewed as a perturbation to the sine-Gordon equation for small amplitude waves, the obstacle to solving the equation for breathers is exponentially small with respect to the amplitude of the breathers. In the talk, we consider a class of Klein-Gordon equation and show that generically there exist small breathers with exponentially small tails.