Abstract
There are a number of mathematical models to nerve pulse propagation in biomembranes, as Hodgkin--Huxley, FitzHugh--Nagumo and Heimburg--Jackson models, see, e.g., [1,2]. However, these models do not describe adequately all observed phenomena.Recently in [2], generalized Boussinesq equation with quadratic--cubic nonlinearity is proposed as an improvement of the well-known Heimburg--Jackson model.In this study we prove analytically the orbital stability and instability of solitary waves to the improved Heimburg--Jackson model (1). The results depend on the relationship between all parameters of the model. For the set of data, obtained experimentally, our theoretical results are in full agreement with the numerical simulations, presented in [3].
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