Framework for the Forced Soliton Equation: Regularization, Numerical Solutions, and Perturbation Theory

TL;DR

This paper introduces analytical and numerical methods for solving the forced soliton equation in two-dimensional models, enabling the study of high momentum transfer phenomena like pair creation and superluminal velocities.

Contribution

It develops regularization techniques, detailed numerical analysis, and perturbation theory for the forced soliton equation in models with kinks, advancing understanding of soliton dynamics.

Findings

Regularization of soliton physics using lattice models.

Numerical solutions show extreme phenomena at high momentum transfer.

Perturbation theory developed for soliton momentum transfer.

Abstract

The forced soliton equation is the starting point for semiclassical computations with solitons away from the small momentum transfer regime. This paper develops necessary analytical and numerical tools for analyzing solutions to the forced soliton equation in the context of two-dimensional models with kinks. Results include a finite degree of freedom regularization of soliton sector physics based on periodic and anti-periodic lattice models, a detailed analysis of numerical solutions, and the development of perturbation theory in the soliton momentum transfer to mass ratio Delta P/M. Numerical solutions at large transfer, greater or similar to the soliton mass, are capable of exhibiting, in a smooth and controlled fashion, extreme phenomena such as soliton-antisoliton pair creation and superluminal collective coordinate velocities, which we investigate.