Determining Static Stresses of Deformed Solitons

TL;DR

This paper develops a covariant variational approach to analyze static stresses and interactions of deformed solitons, specifically applied to the $ ext{Φ}^4$-kink, providing exact solutions and insights into soliton interactions.

Contribution

It introduces a covariant derivation of the quasi-static soliton ansatz for arbitrary collective variables, enabling exact determination of static stresses and intersoliton potentials.

Findings

Exact static stresses of deformed $ ext{Φ}^4$-kink are obtained.

The kink interaction potential at large distances is characterized.

A general method for calculating intersoliton potentials for two-soliton configurations is discussed.

Abstract

An equation for the quasi-static soliton ansatz depending on an arbitrary set of collective variables is covariantly derived on the basis of the variational approach to the method of collective variables. The field configuration and the static stresses of the deformed $\Phi ^4$-kink that are produced by the excitation of the internal soliton mode are exactly determined. The kink interaction potential at large distances is considered for the example of the nonlinear Klein-Gordon system. A general approach to the problem of exactly determining the intersoliton potential for the entire set of physically admissible two-soliton configurations is discussed.