Solitary oscillations and multiple antikink-kink pairs in the double sine-Gordon model

Abstract

We study kink-antikink collisions in a particular case of the double sine-Gordon model depending on only one parameter r. The scattering process of large kink-antikink shows the changing of the topological sector. For some parameter intervals we observed two connected effects: the production of multiple antikink-kink pairs and up to three solitary oscillations. The scattering process for small kink-antikink has several possibilities: the changing of the topological sector, one-bounce collision, two-bounce collision, or formation of a bion state. In particular, we observed for small values of rand velocities, the formation of false two-bounce windows and the suppression of true two-bounce windows, despite the presence of an internal shape mode.

Wobbling double sine-Gordon kinks

“…Therefore, the vibrational mode is not sufficient for the resonant energy exchange mechanism. In [50], the authors obtained a similar result near the integrable limit of a case of the double sine-Gordon different from what is investigated here and, in [62], the authors also found false resonance windows near the integrable regime of a deformed sine-Gordon model. We searched carefully for resonance windows with precision ∆v i = 10 −5 and no resonance windows were found.…”

“…However, to leading order, a conservative perturbation to the sine-Gordon model still has a trivial kink-antikink collision [47]. Other important works about kink collisions in this model include [13,41,[48][49][50]. An important feature that appears in these works is that the kinks have an inner structure, i.e., it consists of two subkinks, which may be exchanged at collision and form subkink bound states.…”

Exotic final states in the $$\varphi ^8$$ multi-kink collisions

“…Kinkantikink pair creation, as a result of the excitation of the vibrational mode of the ϕ 4 kink, was observed in [32]. Production of antikink-kink pairs and solitary oscillating structures was also found in the double sine-Gordon model [27].…”

“…Returning to the scattering of kinks in (1 + 1)-dimensional field-theoretic models, we mention the formation of oscillons -moving or static oscillating structures localized in space, which also can form bound states. Escaping oscillons, as well as bound states of oscillons, have been observed, e.g., in the sinh-deformed ϕ 4 and the double sine-Gordon models [24][25][26][27]. Formation of oscillons in kink-antikink collisions was also found in hyperbolic models [28] and in a parametrized ϕ 4 model [29].…”

Relativistic Moduli Space for Kink Collisions

“…Except in the rare cases of integrable theories, many aspects of soliton scattering are still far from being fully understood. Among these is the fractal velocity-dependence of the final state in kinkantikink collisions, associated with the resonant coupling of translational motion to oscillating modes [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], which can be normal or quasi-normal modes [21] hosted by free solitons, or the internal modes hosted by ephemeral configurations occurring during the collision [22,23]. Also intriguing is the recently discovered spectral wall phenomenon [24,25], caused by the transition of a normal mode into the continuum spectrum as solitons approach each other.…”