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The evolution of nonlinear waves in active media. (English) Zbl 0572.73038

An evolution equation that describes the behaviour of single waves in active media is derived. The basic mathematical model corresponds to pulse transmission in nerve fibers according to the hyperbolic telegraph equation. A numerical experiment is carried out in which the evolution equation is solved by the pseudospectral method and the corresponding stationary wave equation by the standard Runge-Kutta method. The evolution equation has a stationary solution in the form of an unsymmetric solitary wave with a refractive tail. The numerical simulation of the process gives physically admissible results, namely, the suitable wave profile and the existence of the threshold and asymptotic values. The situation analyzed here in an active medium with energy influx is in a certain sense similar to the formation of solitary waves in a conservative medium.

MSC:

74J99 Waves in solid mechanics
92Cxx Physiological, cellular and medical topics
35L05 Wave equation
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