TY - JOUR
T1 - Application of the Exp(−φ(ξ))-Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves
AU - Rani, Attia
AU - Shakeel, Muhammad
AU - Kbiri Alaoui, Mohammed
AU - Zidan, Ahmed M.
AU - Shah, Nehad Ali
AU - Junsawang, Prem
N1 - Funding Information:
The authors extends their appreciation to the Deanship of Scientific Research at King Khalid University, Abha 61413, Saudi Arabia, for funding this work through a research group program under grant number R.G.P.-2/65/43. This research received funding support from the NSRF via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation, (grant number B05F650018).
Publisher Copyright:
© 2022 by the authors.
PY - 2022/9
Y1 - 2022/9
N2 - 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 (Formula presented.) -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.
AB - 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 (Formula presented.) -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.
KW - exp(−φ(ξ))-expansion method
KW - Heimburg model
KW - nonlinear partial differential equations
KW - traveling wave solutions
UR - http://www.scopus.com/inward/record.url?scp=85138636900&partnerID=8YFLogxK
U2 - 10.3390/math10183372
DO - 10.3390/math10183372
M3 - Article
AN - SCOPUS:85138636900
SN - 2227-7390
VL - 10
JO - Mathematics
JF - Mathematics
IS - 18
M1 - 3372
ER -