Eur. Phys. J. Plus (2019) 134: 200
https://doi.org/10.1140/epjp/i2019-12544-y

Regular Article

Exact solutions of semi-discrete sine-Gordon equation

Department of Physics, University of the Punjab, Quaid-e-Azam Campus, 54590, Lahore, Pakistan

^* e-mail: yasir_pmc@yahoo.com

Received: 15 October 2018
Accepted: 26 January 2019
Published online: 13 May 2019

Abstract

In this paper, we study a semi-discrete sine-Gordon (sd-SG) equation and compute various types of solutions analytically. We apply Darboux transformation to the associated spectral problem and construct N-soliton solutions of sd-SG equation in terms of ratio of ordinary determinants. In addition, we also construct explicit expressions of discrete one-kink, two-kink, kink-antikink, breather and degenerate soliton solutions of sd-SG equation in zero background.