Coupled sine-Gordon systems in living cellular structure

Abstract

In this paper, we present a coupled sine-Gordon (CSG) system, which describes the dynamics of two deoxyribonucleic acid (DNA) twisting strands in open configuration. We investigate the associated linear eigenvalue problem of the CSG system and obtain generalized formulae for multiple soliton solutions by employing the Darboux transformation (DT). Explicit expressions of one- and two-kink and line soliton solutions, single breather and first-order degenerate solutions are obtained by using particular solutions to the associated linear eigenvalue problem. We also present the dynamics of the different solutions.