The talk concerns stability properties of kinks for (1+1)-dimensional nonlinear scalar field models of the form \[\partial_t^2 \phi - \partial_x^2 \phi + W'(\phi) = 0 \quad (t,x) \in {\bf \mathbb R}\times {\mathbb R}.\] We establish a simple and explicit sufficient condition on the potential $W$ for the asymptotic stability of a given moving or standing kink. We present applications of the criterion to some models of the Physics literature.

Work in collaboration with Michał Kowalczyk, Claudio Muñoz and Hanne Van Den Bosch.

See also the related work with Michał Kowalczyk and Claudio Muñoz.