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<p>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 ∆<i>P</i>/<i>M</i>. Numerical solutions at large transfer ∆<i>P</i> ≳ <i>M</i> 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.</p>

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Framework for the forced soliton equation: regularization, numerical solutions, and perturbation theory

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月15日

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  • Zachary J. Allamon,
  • Quentin A. Hales,
  • Andrew B. Royston,
  • Douglas L. Rutledge,
  • Erica A. Yozie

摘要

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 ∆P/M. Numerical solutions at large transfer ∆P ≳ M 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.