Applied Mathematics Seminar
Avy Soffer
Rudgers University
Long Range Scattering for the Klein-Gordon equation with variable coefficient nonlinearities
Abstract: The asymptotic stability of coherent states , like kinks in one dimension, poses a great
challenge. This is due to the long range nature of the dispersive equation. This
talk will focus on one such problem. We study the 1D Klein-Gordon equation with quadratic and
variable coefficient cubic nonlinearity. This problem exhibits a striking resonant interaction between
the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the
solutions. We prove global existence and (in L-infinity) scattering as well as a certain kind of
strong smoothness for the solution at time-like infinity; it is based on several new classes of
normal-form transformations. The analysis also shows the limited smoothness of the solution,
in the presence of the resonances.
Monday April 20, 2015 at 4:00 PM in SEO 636