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

Christov, Ivan C.; Decker, Robert J.; Demirkaya, A.; Gani, Vakhid A.; Kevrekidis, P. G.; Saxena, Avadh Behari

doi:10.1016/j.cnsns.2021.105748

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

Journal Article · Tue Feb 02 00:00:00 EST 2021 · Communications in Nonlinear Science and Numerical Simulation

DOI:https://doi.org/10.1016/j.cnsns.2021.105748· OSTI ID:1765871

^[1]; Decker, Robert J. ^[2]; Demirkaya, A. ^[2];

^[3];

^[4];

^[5]

Purdue Univ., West Lafayette, IN (United States)
Univ. of Hartford, West Hartford, CT (United States)
Moscow Engineering Physics Inst. (MEPhI), Moscow (Russia); National Research Centre, Moscow (Russian Federation). Kurchatov Institute
Univ. of Massachusetts, Amherst, MA (United States); Univ. of Oxford (United Kingdom)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

In this work, we study collisions of coherent structures in higher-order field-theoretic models, such as the Φ⁸, Φ¹⁰ and Φ¹² 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 Φ⁴ and Φ⁶ 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.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); Russian Foundation for Basic Research (RFBR); National Science Foundation (NSF)

Grant/Contract Number:: 89233218CNA000001; 19-02-00971; PHY-1602994; DMS-1809074

OSTI ID:: 1765871

Report Number(s):: LA-UR-20-23167; TRN: US2206274

Journal Information:: Communications in Nonlinear Science and Numerical Simulation, Vol. 97; ISSN 1007-5704

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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