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

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).


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
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