Kink-antikink collisions and multi-bounce resonance windows in higher-order field theories

We study collisions of coherent structures in higher-order field-theoretic models, such as the phi(8), phi(10) and phi(12) ones. The main distinguishing feature, of the example models considered herein, is that the collision arises due to the long-range interacting algebraic tails of these solitary waves. We extend the approach to suitably initialize the relevant kinks, in the additional presence of finite initial velocity, in order to minimize the dispersive wave radiation potentially created by their slow spatial decay. We find that, when suitably initialized, these models still feature the multi-bounce resonance windows earlier found in models in which the kinks bear exponential tails, such as the phi(4) and phi(6) field theories among others. Also present is the self-similar structure of the associated windows with three- and more-bounce windows at the edges of two- and lower-bounce ones. Moreover, phenomenological but highly accurate (and predictive), scaling relations are derived for the dependence of the time between consecutive collisions and, e.g., the difference in kinetic energy between the incoming one and the critical one for one-bounces. Such scalings are traced extensively over two-bounce collision windows throughout the three models, hinting at the possibility of an analytical theory in this direction. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

The study focuses on collisions of coherent structures in higher-order field-theoretic models, highlighting the long-range interacting algebraic tails of solitary waves as the main distinguishing feature. The models, when suitably initialized, still exhibit multi-bounce resonance windows, with a self-similar structure and scaling relations derived for time between consecutive collisions and differences in kinetic energy. The extensive tracing of these scalings throughout two-bounce collision windows hints at the potential for an analytical theory in this direction.