Eur. Phys. J. B (2018) 91: 22
https://doi.org/10.1140/epjb/e2017-80406-y

Regular Article

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

¹ Department of Physics, Quchan Branch, Islamic Azad University, Quchan, Iran
² Department of Physics, Ferdowsi University of Mashhad, 91775-1436 Mashhad, Iran
³ Department of Physics, University of Sistan and Baluchestan, Zahedan, Iran
⁴ Institute for Metals Superplasticity Problems RAS, Khalturin Street 39, 450001 Ufa, Russia
⁵ National Research Tomsk State University, Lenin Ave. 36, 634050 Tomsk, Russia

^a e-mail: moradimarjaneh@gmail.com

Received: 9 July 2017
Received in final form: 24 October 2017
Published online: 25 January 2018

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 ≤ N ≤ 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.