Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions

TL;DR

This paper analyzes the maximum elastic strain and energy components during multi-kink collisions in the sine-Gordon model, revealing elastic strain as the dominant energy contributor and larger tensile than compressive strains.

Contribution

It provides detailed analysis of potential energy components and elastic strain extremes in multi-kink collisions, extending previous work on total energy densities.

Findings

Elastic strain is the main contributor to potential energy density.

Tensile strain exceeds compressive strain in multi-soliton collisions.

The study offers new insights into energy distribution during kink interactions.

Abstract

In our recent study the maximal values of kinetic and potential energy densities that can be achieved in the collisions of $N$ slow kinks in the sine-Gordon model were calculated analytically (for $N=1,2$, and 3) and numerically (for $4\le N\le 7$). However, for many physical applications it is important to know not only the total potential energy density but also its two components (the on-site potential energy density and the elastic strain energy density) as well as the extreme values of the elastic strain, tensile (positive) and compressive (negative). In the present study we give (i) the two components of the potential energy density and (ii) the extreme values of elastic strain. Our results suggest that in multi-soliton collisions the main contribution to the potential energy density comes from the elastic strain, but not from the on-site potential. It is also found that tensile strain is usually larger than compressive strain in the core of multi-soliton collision.