Lambert W-kink Solitons Arising from Higher-Order Nonlinearities of Lipid Membranes

TL;DR

This paper introduces Lambert W-kink solitons derived from higher-order nonlinearities in lipid membranes, enhancing the understanding of nerve impulse propagation through advanced mathematical modeling.

Contribution

It presents a novel class of Lambert W-kink solitons obtained from a generalized Duffing equation incorporating higher-order nonlinearities in membrane dynamics.

Findings

Derivation of exact traveling wave solutions including Lambert W-kink solitons

Enhanced modeling of nerve membrane nonlinear electromechanical behavior

Analytical insights into pulse propagation mechanisms in biomembranes

Abstract

Accurate modelling of nerve impulse propagation requires accounting for strong higher-order nonlinearities in membrane dynamics, as incorporated in the extended Heimburg-Jackson model. By introducing third- and fourth-order polynomial terms into the membrane density equation, we derive a generalized Duffing-type equation that better captures the complex biophysical states involved in signal transmission. Applying the factorization method, we construct exact travelling wave solutions, including a novel class of Lambert W-Kink-type solitons. These findings provide new analytical insight into the nonlinear electromechanical behaviour of nerve membranes and contribute to the theoretical foundation for understanding pulse propagation in biomembranes.