Sine-Gordon solitons, kinks and breathers as physical models of nonlinear excitations in living cellular structures. (English) Zbl 1292.82040

Ivancevic, Vladimir G.; Ivancevic, Tijana T.

J. Geom. Symmetry Phys. 31, 1-56 (2013).

Summary: 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).

MSC:

82Dxx	Applications of statistical mechanics to specific types of physical systems
92B20	Neural networks for/in biological studies, artificial life and related topics
35Q51	Soliton equations
35Q53	KdV equations (Korteweg-de Vries equations)
35C08	Soliton solutions
92C37	Cell biology
92D20	Protein sequences, DNA sequences
92C20	Neural biology
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K40	Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems

Keywords:

DNA; protein folding; sine-Gordon equation; Korteweg-de Vries; nonlinear Schrödinger equations; solitons, kinks and breathers; Lax-pair; integrability