Lambert W-kink Solitons Arising from Higher-Order Nonlinearities of Lipid Membranes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915407673163776 |
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| author | Mendoza-Millán, V. A. Larios-Ferrer, J. L. Millán, J. Samuel Pavón-Torres, O. |
| author_facet | Mendoza-Millán, V. A. Larios-Ferrer, J. L. Millán, J. Samuel Pavón-Torres, O. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lambert W-kink Solitons Arising from Higher-Order Nonlinearities of Lipid Membranes Mendoza-Millán, V. A. Larios-Ferrer, J. L. Millán, J. Samuel Pavón-Torres, O. Biological Physics Pattern Formation and Solitons Quantum Physics 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. |
| title | Lambert W-kink Solitons Arising from Higher-Order Nonlinearities of Lipid Membranes |
| topic | Biological Physics Pattern Formation and Solitons Quantum Physics |
| url | https://arxiv.org/abs/2507.17965 |