Adiabatic evolution of solitons embedded in lipid membranes

Abstract The Heimburg-Jackson model, or thermodynamic soliton theory of nervous impulses, has a well-established record as an alternative model for studying the dynamics of nerve impulses and lipid membranes. Within this framework, nerve impulses can be represented as nonlinear excitations of low amplitude depicted by the damped nonlinear Schrödinger equation and their adiabatic evolution can be analyzed using direct perturbative methods. Based on the foregoing, we carry out the current study using the quasi-stationary approach to obtain the adiabatic evolution of solitons embedded in lipid membranes under the influence of a viscous elastic fluid. This analysis encompasses liquid-to-gel transition of the lipid bilayers, for whose dark and bright solitons arise, respectively.