Asymptotics for 1D Klein-Gordon equations with variable coefficient quadratic nonlinearities.

Abstract:

The problem of the asymptotic stability of kinks in classical nonlinear scalar field equations on the real line leads to the study of the decay of small solutions to 1D Klein-Gordon equations with variable coefficient quadratic nonlinearities. I will discuss the occurrence of a novel modified scattering behavior of such solutions that involves a logarithmic slow-down of the decay rate along certain rays. It is caused by a striking resonant interaction between specific spatial frequencies of the variable coefficient and the temporal oscillations of the solutions.

This talk is based on joint work with H. Lindblad and A. Soffer.

Posted on Nov 4, 2020 in Differential Equations, Seminars