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Keywords = Heimburg model

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12 pages, 2498 KB  
Article
Application of the Expφξ-Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves
by Attia Rani, Muhammad Shakeel, Mohammed Kbiri Alaoui, Ahmed M. Zidan, Nehad Ali Shah and Prem Junsawang
Mathematics 2022, 10(18), 3372; https://doi.org/10.3390/math10183372 - 16 Sep 2022
Cited by 33 | Viewed by 2956
Abstract
Heimburg and Jackson devised a mathematical model known as the Heimburg model to describe the transmission of electromechanical pulses in nerves, which is a significant step forward. The major objective of this paper was to examine the dynamics of the Heimburg model by [...] Read more.
Heimburg and Jackson devised a mathematical model known as the Heimburg model to describe the transmission of electromechanical pulses in nerves, which is a significant step forward. The major objective of this paper was to examine the dynamics of the Heimburg model by extracting closed-form wave solutions. The proposed model was not studied by using analytical techniques. For the first time, innovative analytical solutions were investigated using the expφξ-expansion method to illustrate the dynamic behavior of the electromechanical pulse in a nerve. This approach generates a wide range of general and broad-spectral solutions with unknown parameters. For the definitive value of these constraints, the well-known periodic- and kink-shaped solitons were recovered. By giving different values to the parameters, the 3D, 2D, and contour forms that constantly modulate in the form of an electromechanical pulse traveling through the axon in the nerve were created. The discovered solutions are innovative, distinct, and useful and might be crucial in medicine and biosciences. Full article
(This article belongs to the Special Issue Partial Differential Equations with Applications: Analytical Methods)
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