Some Recent Developments on Kink Collisions and Related Topics

Abstract

We review recent works on modeling of dynamics of kinks in 1+1 dimensional ${\varphi }^4$ theory and other related models, like sine-Gordon model or ${\varphi }^6$ theory. We discuss how the spectral structure of small perturbations can affect the dynamics of non-perturbative states, such as kinks or oscillons. We describe different mechanisms, which may lead to the occurrence of the resonant structure in the kink-antikink collisions. We explain the origin of the radiation pressure mechanism, in particular, the appearance of the negative radiation pressure in the ${\varphi }^4$ and ${\varphi }^6$ models. We also show that the process of production of the kink-antikink pairs, induced by radiation is chaotic.

26 pages, 9 figures; invited chapter to "A dynamical perspective on the ϕ4 model: Past, present and future", Eds. P.G. Kevrekidis and J. Cuevas-Maraver; Springer book class with svmult.cls included