Sine--Gordon Solitons, Kinks and Breathers as Physical Models of Nonlinear Excitations in Living Cellular Structures

Abstract

Nonlinear space-time dynamics, defined in terms of celebrated `solitonic` equations, brings indispensable tools for understanding, prediction and control of complex behaviors in both physical and life sciences. In this paper, we review sine--Gordon solitons, kinks and breathers as models of nonlinear excitations in complex systems in physics and in living cellular structures, both intra--cellular (DNA, protein folding and microtubules) and inter--cellular (neural impulses and muscular contractions).