Scattering of the double sine-Gordon kinks

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.Comment: 12 pages, 7 figures; v2: minor changes to match version published in EPJ

High energy density spots and production of kink–antikink pairs in particle collisions

Creation of solitons as kink–antikink pairs from particles is investigated, in the model. Particle-like states are simulated by two widely separated identical wave trains which are propagated toward collision point from both sides in a trivial background. The maximal energy density that can be achieved in the collisions of the particle-like wave trains is investigated numerically for different wave train parameters. Maximum energy and number of kink–antikink pairs created after the collision is calculated and the relation between them are studied. It is shown numerically that, if the number of created kink–antikink pairs are N, the maximal energy density should be at least equal to N2/2

Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions

In our recent study the maximal values of kinetic and potential energy densities that can be achieved in the collisions of N slow kinks in the sine-Gordon model were calculated analytically (for N = 1, 2, and 3) and numerically (for 4 ≤ N ≤ 7). However, for many physical applications it is important to know not only the total potential energy density but also its two components (the on-site potential energy density and the elastic strain energy density) as well as the extreme values of the elastic strain, tensile (positive) and compressive (negative). In the present study we give (i) the two components of the potential energy density and (ii) the extreme values of elastic strain. Our results suggest that in multi-soliton collisions the main contribution to the potential energy density comes from the elastic strain, but not from the on-site potential. It is also found that tensile strain is usually larger than compressive strain in the core of multi-soliton collision