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Controlled complexity in pulse conduction: traveling solitons from neural to optical fibers. (English) Zbl 1366.35178

Authors’ abstract: We review and analyze models of controlled complexity in nonlinear pulse conduction, ranging from the Hodgkin-Huxley action potentials propagating along neural fibers to rogue waves in optical fibers. The novel model proposed is an alternative to the Hodgkin-Huxley neural model in the form of the sine-Gordon wave equation. This new alternative explains pulse conduction in terms of general wave phenomena (such as kinks, solitons and breathers).

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
78A70 Biological applications of optics and electromagnetic theory
78A60 Lasers, masers, optical bistability, nonlinear optics
92C20 Neural biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
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