Application of the Exp − φ ξ -Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves

Attia Rani, Muhammad Shakeel, Mohammed Kbiri Alaoui, Ahmed M. Zidan, Nehad Ali Shah and Prem Junsawang ()
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Attia Rani: Department of Mathematics, University of Wah, Wah Cantt 47040, Pakistan
Muhammad Shakeel: Department of Mathematics, University of Wah, Wah Cantt 47040, Pakistan
Mohammed Kbiri Alaoui: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
Ahmed M. Zidan: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
Nehad Ali Shah: Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
Prem Junsawang: Department of Statistics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Mathematics, 2022, vol. 10, issue 18, 1-12

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 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 exp − φ ξ -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.

Keywords: nonlinear partial differential equations; exp(? ? ( ? ))-expansion method; Heimburg model; traveling wave solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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