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.

Oscillons in hyperbolic models

“…The study of collisions of kink and antikink has gained further attention recently, with the study of polynomial models with one [8,[10][11][12] and two or more [14][15][16][17] scalar fields, of nonpolynomial models [18][19][20][21] and of models that support multi-kink configurations [22][23][24][25]. Moreover, there are investigations on the collision of large relativistic bubbles, that can be treated as that of planar walls, described as kink scattering in (1, 1) dimensions [26].…”

Kink scattering in hyperbolic models

“…Recently there has been a renewal of the study of kink and antikink scattering, with several models being subject of investigation. In this line one can cite polynomial models with one [14,[17][18][19][20][21][22][23][24] and two or more [25][26][27][28] scalar fields, nonpolynomial models [29][30][31][32][33][34] and multi-kinks [35][36][37][38][39].…”

Collision of two kinks with inner structure

“…One of the interesting phenomena is the escape of two bions, which has been found and discussed in many models such as the double Sine-Gordon model [47,57,77], the sinh-deformed φ 4 model [48] and other models with double kinks [95,100]. In previous works, two-bion final states are usually generated by colliding a pair of double kinks.…”

“…Recently, more and more works began to investigate kink interaction in other nonintegrable models, such as models with higher-order polynomial potentials [34][35][36][37][38][39][40][41][42], with various kinds of triangular potentials [43][44][45][46][47][48][49], with generalized dynamics [50], and with multi-component scalar fields [51][52][53][54][55][56].…”