Scattering of the double sine-Gordon kinks

Abstract

We study the scattering of kink and antikink of the double sine-Gordon model. There is a critical value of the initial velocity $v_{cr}$ of the colliding kinks, which separates different regimes of the collision. At $v_{in}>v_{cr}$ we observe kinks reflection, while at $v_{in}<v_{cr}$ their interaction is complicated with capture and escape windows. We obtain the dependence of $v_{cr}$ on the parameter of the model. This dependence possesses a series of local maxima, which has not been reported by other authors. At some initial velocities below the critical value we observe a new phenomenon -- the escape of two oscillons in the final state. Besides that, at $v_{in}<v_{cr}$ we found the initial kinks' velocities at which the oscillons do not escape, and the final configuration looks like a bound state of two oscillons.