Soliton dynamics in the ABS nonlinear spinor model with external fields

TL;DR

This paper investigates the dynamics of solitons in a novel (1+1)-dimensional nonlinear Dirac spinor model with external potentials, developing a collective coordinates approach and confirming results through numerical simulations.

Contribution

It introduces a collective coordinates framework for the ABS nonlinear spinor model and compares its soliton dynamics to the Gross-Neveu model, supported by numerical validation.

Findings

Soliton dynamics in the ABS model are qualitatively similar to the Gross-Neveu model.

The collective coordinates approach accurately predicts soliton behavior under various potentials.

Numerical simulations confirm the theoretical predictions of the collective coordinates theory.

Abstract

We consider the novel nonlinear model in (1 + 1)-dimensions for Dirac spinors recently introduced by Alexeeva, Barashenkov, and Saxena [1] (ABS model), which admits an exact explicit solitary-wave (soliton for short) solution. The charge, the momentum, and the energy of this solution are conserved. We investigate the dynamics of the soliton subjected to several potentials: a ramp, a harmonic, and a periodic potential. We develop a Collective Coordinates Theory by making an ansatz for a moving soliton where the position, rapidity, and momentum, are functions of time. We insert the ansatz into the Lagrangian density of the model, integrate over space and obtain a Lagrangian as a function of the collective coordinates. This Lagrangian differs only in the charge and mass with the Lagrangian of a collective coordinates theory for the Gross-Neveu equation. Thus the soliton dynamics in the ABS spinor model is qualitatively the same as in the Gross-Neveu equation, but quantitatively it differs. These results of the collective coordinates theory are confirmed by simulations, i.e., by numerical solutions for solitons of the ABS spinor model, subjected to the above potentials.