Kink-antikink collisions for twin models

Abstract

In this work we consider kink-antikink collisions for some classes of $(1,1)$-dimensional nonlinear models. We are particularly interested to investigate in which aspect the presence of a general kinetic content in the Lagrangian could be revealed in a collision process. We consider a particular class of models known as twin theories, where different models lead to same solutions for the equations of motion and same energy density profile. The theories can be distinguished in the level of linear stability of defect structure. We study a class of k-defect theories depending on a parameter $M$ which is the twin theory of the usual $ϕ^4$ theory with standard dynamics. For $M\to\infty$ both models are characterized by the same potential. In the regime $1/M^2<<1$, we obtain analytically the spectrum of excitations around the kink solution. It is shown that with the increasing on the parameter $1/M^2$: i) the gap between the zero-mode and the first-excited mode increases and ii) the tendency of one-bounce collision between kink-antikink increases. We numerically investigate kink-antikink scattering, looking for the influence of the parameter changing for the thickness and number of two-bounce windows, and confronting the results with our analytical findings.