Framework for the Forced Soliton Equation: Regularization, Numerical Solutions, and Perturbation Theory
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.
Cite
@article{arxiv.2412.09487,
title = {Framework for the Forced Soliton Equation: Regularization, Numerical Solutions, and Perturbation Theory},
author = {Zachary J. Allamon and Quentin A. Hales and Andrew B. Royston and Douglas L. Rutledge and Erica A. Yozie},
journal= {arXiv preprint arXiv:2412.09487},
year = {2025}
}
Comments
v1: 74 pages plus appendices; 18 figures. v2: 77 pages plus appendices; 19 figures; typos corrected; details added and examples updated in Subsection 4.2; Mathematica notebook included as ancillary file