The volume of a soliton

TL;DR

This paper establishes that the geometric volume of a soliton uniquely matches its thermodynamical volume, providing a consistent and universal definition applicable across various dimensions and soliton types.

Contribution

It demonstrates that the geometric volume of a soliton can be uniquely defined and coincides with its thermodynamical volume in general settings.

Findings

Geometric volume coincides with thermodynamical volume for solitons.

The volume definition is applicable to arbitrary solitons in any dimension.

Provides a universal volume concept for solitons.

Abstract

There exists, in general, no unique definition of the size (volume, area, etc., depending on dimension) of a soliton. Here we demonstrate that the geometric volume (area etc.) of a soliton is singled out in the sense that it exactly coincides with the thermodynamical or continuum-mechanical volume. In addition, this volume may be defined uniquely for rather arbitrary solitons in arbitrary dimensions.