A Sufficient Condition for Asymptotic Stability of Kinks in General (1+1)-Scalar Field Models

We study stability properties of kinks for the (1+1)-dimensional nonlinear scalar field theory models $$\begin{aligned} \partial _t^2\phi -\partial _x^2\phi + W'(\phi ) = 0, \quad (t,x)\in \mathbb {R}\times {R}. \end{aligned}$$ The orbital under general assumptions on potential W is a consequence energy arguments. Our main result derivation simple and explicit sufficient condition asymptotic given kink. This applies to any static or moving kink, in particular no symmetry assumption required. Last, motivated by Physics literature, we present applications criterion $$P(\phi )_2$$ theories double sine-Gordon theory.