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.

Abstract. 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 multisoliton 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.PACS. 05.45.Yv Solitons -11.10.Lm Nonlinear or nonlocal theories and models -45.50.Tn Collisions

The maximal energy density that can be achieved in the collisions of the particle-like wave trains in the φ 4 model has been investigated numerically for different wave train parameters. From these results the prediction is made on how many kink-antikink pairs can be produced in wave train collisions taking into account that in collision of N kinks maximal energy density is equal to N 2 /2 for even N. Our numerical results are in a reasonably good agreement with the predicted maximal number of kink-antikink pairs formed in wave train collisions.

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