Collective coordinates method for long-range kink collisions

TL;DR

This paper develops a collective coordinates approach to analyze long-range kink collisions in potentials with three minima, comparing effective Lagrangian results with full dynamical simulations.

Contribution

It introduces a novel collective coordinate framework for long-range kink interactions, including a generalized Derrick mode and impurity ansatz, enhancing understanding of complex soliton dynamics.

Findings

Effective Lagrangian captures kink-antikink interactions accurately.

Generalized Derrick mode provides insight into wobbling kink interactions.

Comparison shows good agreement between analytical and numerical results.

Abstract

In this paper, we explored a class of potentials with three minima that support kink solutions exhibiting one long-range tail. We analyzed antikink-kink interactions using an effective Lagrangian based on collective coordinates and compared the results to those obtained from full dynamical simulations. To this end, we constructed the collective coordinates with the antikink-kink configuration, and also a generalized Derrick mode, choosing the kink position and the Derrick mode amplitude as the moduli. For the antikink-kink configuration, we utilized the impurity ansatz proposed in \cite{campos2024collision}. We also studied the interaction of wobbling kinks where the lowest delocalized mode is excited.