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_{{mathrm {cr}}} of the colliding kinks, which separates different regimes of the collision. At v_{mathrm {in}}>v_{mathrm {cr}} we observe kinks reflection, while at v_{mathrm {in}}<v_{mathrm {cr}} their interaction is complicated with capture and escape windows. We obtain the dependence of v_{mathrm {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_{mathrm {in}}<v_{mathrm {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.
Highlights
Kink–antikink collisions, as well as interactions of kinks with impurities, are of growing interest since 1970s [21,22]
In this paper we study the kink-antikink collisions within the double sine-Gordon model [36], [64,65,66]
The potential of the double sine-Gordon (DSG) model can be written in several different forms
Summary
Kink–antikink collisions, as well as interactions of kinks with impurities (spatial inhomogeneities), are of growing interest since 1970s [21,22]. The more complicated modifications of the method have been elaborated, which include other degrees of freedom (in particular, vibrational), see, e.g., [24,25,26] Another approximate method for investigating the kinks interactions is Manton’s method [3, Ch. 5], [32,33,34,35]. For the non-negative potential V (φ) we can introduce the superpotential – a smooth (continuously differentiable) function W (φ) of the field φ:. Using this representation of the potential, the energy of a static configuration can be written as. In some cases we use “kink” for both solutions, just to be brief
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
