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

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  • Mendoza-Millán, V.A.
  • Larios-Ferrer, J.L.
  • Millán, J. Samuel
  • Agüero-Granados, M.A.
  • Galván-Arellano, D.M.
  • Pavón-Torres, O.

Abstract

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.

Suggested Citation

  • Mendoza-Millán, V.A. & Larios-Ferrer, J.L. & Millán, J. Samuel & Agüero-Granados, M.A. & Galván-Arellano, D.M. & Pavón-Torres, O., 2025. "Lambert W-Kink solitons arising from higher-order nonlinearities of lipid membranes," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p2:s0960077925012731
    DOI: 10.1016/j.chaos.2025.117260
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    References listed on IDEAS

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    1. Attia Rani & Muhammad Shakeel & Mohammed Kbiri Alaoui & Ahmed M. Zidan & Nehad Ali Shah & Prem Junsawang, 2022. "Application of the Exp − φ ξ -Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves," Mathematics, MDPI, vol. 10(18), pages 1-12, September.
    2. Oswaldo González-Gaxiola & Anjan Biswas & Luminita Moraru & Abdulah A. Alghamdi, 2023. "Solitons in Neurosciences by the Laplace–Adomian Decomposition Scheme," Mathematics, MDPI, vol. 11(5), pages 1-13, February.
    3. Ahmed El Hady & Benjamin B. Machta, 2015. "Mechanical surface waves accompany action potential propagation," Nature Communications, Nature, vol. 6(1), pages 1-7, November.
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