Lambert W-Kink solitons arising from higher-order nonlinearities of lipid membranes

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Accurate modelling of electromechanical wave propagation in lipid membranes requires accounting for higher-order nonlinearities, 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. • Factorization method used to solve the generalized Boussinesq equation. • Extended Heimburg–Jackson model reduced to a generalized Duffing equation. • Lambert W-kink solitons analyzed and compared with standard kink solutions. • Analytical study determines elastic constants from higher-order nonlinearities. • Equivalence shown between factorization and G ′ / G -expansion methods.