Interaction for Solitary Waves with a Phase Difference in a Nonlinear Dirac Model

TL;DR

This study numerically investigates the interaction dynamics of solitary waves with phase differences in a nonlinear Dirac model, revealing phenomena like repulsion, attraction, collapse, and overlap interactions.

Contribution

It introduces a high-accuracy numerical approach to analyze complex solitary wave interactions in a nonlinear Dirac field with phase differences.

Findings

Full repulsion in binary and ternary collisions depending on initial distance

Sequential repulsion and attraction leading to collapse in resting wave collisions

Observation of one-overlap and two-overlap interactions in ternary collisions

Abstract

This paper presents a further numerical study of the interaction dynamics for solitary waves in a nonlinear Dirac field with scalar self-interaction by using a fourth order accurate Runge-Kutta discontinuous Galerkin method. Our experiments are conducted on the Dirac solitary waves with a phase difference. Some interesting phenomena are observed: (a) full repulsion in binary and ternary collisions and its dependence on the distance between initial waves; (b) repulsing first, attracting afterwards, and then collapse in binary and ternary collisions of initially resting two-humped waves; (c) one-overlap interaction and two-overlap interaction in ternary collisions of initially resting waves.