Michal Kowalczyk

Universidad de Chile

A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models

In this talk I will discuss stability properties of kinks for the (1+1)-dimensional nonlinear scalar field theory models

\[\partial_t^2\phi -\partial_x^2\phi + W'(\phi) = 0, \quad (t,x)\in\mathbb R\times\mathbb R.\]

The orbital stability of kinks under general assumptions on the potential \(W\) is a consequence of energy arguments. The main result I will present is the derivation of a simple and explicit sufficient condition on the potential \(W\) for the asymptotic stability of a given kink. This condition applies to any static or moving kink, in particular no symmetry assumption is required. Applications of the criterion to the \(P(\phi)_2\) theories and the double sine-Gordon theory will be discussed.

This is a joint work with Y. Martel, C. Muñoz and H. Van Den Bosch.