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).
Vladimir G. Ivancevic. Tijana T. Ivancevic. "Sine--Gordon Solitons, Kinks and Breathers as Physical Models of Nonlinear Excitations in Living Cellular Structures." J. Geom. Symmetry Phys. 31 1 - 56, 2013. https://doi.org/10.7546/jgsp-31-2013-1-56