Application of the Exp<inline-formula><math display="inline"><semantics><mrow><mfenced><mrow><mo>−</mo><mi>φ</mi><mfenced><mi>ξ</mi></mfenced></mrow></mfenced></mrow></semantics></math></inline-formula>-Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves
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 so...
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/18/3372 |
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| author | Attia Rani Muhammad Shakeel Mohammed Kbiri Alaoui Ahmed M. Zidan Nehad Ali Shah Prem Junsawang |
| author_facet | Attia Rani Muhammad Shakeel Mohammed Kbiri Alaoui Ahmed M. Zidan Nehad Ali Shah Prem Junsawang |
| author_sort | Attia Rani |
| collection | DOAJ |
| description | 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<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced><mrow><mo>−</mo><mi>φ</mi><mfenced><mi>ξ</mi></mfenced></mrow></mfenced></mrow></semantics></math></inline-formula>-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. |
| first_indexed | 2024-03-09T23:14:43Z |
| format | Article |
| id | doaj.art-7417a998efb545ad9eb2b4a554558831 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:14:43Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7417a998efb545ad9eb2b4a5545588312023-11-23T17:37:38ZengMDPI AGMathematics2227-73902022-09-011018337210.3390/math10183372Application of the Exp<inline-formula><math display="inline"><semantics><mrow><mfenced><mrow><mo>−</mo><mi>φ</mi><mfenced><mi>ξ</mi></mfenced></mrow></mfenced></mrow></semantics></math></inline-formula>-Expansion Method to Find the Soliton Solutions in Biomembranes and NervesAttia Rani0Muhammad Shakeel1Mohammed Kbiri Alaoui2Ahmed M. Zidan3Nehad Ali Shah4Prem Junsawang5Department of Mathematics, University of Wah, Wah Cantt 47040, PakistanDepartment of Mathematics, University of Wah, Wah Cantt 47040, PakistanDepartment of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi ArabiaDepartment of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi ArabiaDepartment of Mechanical Engineering, Sejong University, Seoul 05006, KoreaDepartment of Statistics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandHeimburg 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<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced><mrow><mo>−</mo><mi>φ</mi><mfenced><mi>ξ</mi></mfenced></mrow></mfenced></mrow></semantics></math></inline-formula>-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.https://www.mdpi.com/2227-7390/10/18/3372nonlinear partial differential equationsexp(−<i>φ</i>(<i>ξ</i>))-expansion methodHeimburg modeltraveling wave solutions |
| spellingShingle | Attia Rani Muhammad Shakeel Mohammed Kbiri Alaoui Ahmed M. Zidan Nehad Ali Shah Prem Junsawang Application of the Exp<inline-formula><math display="inline"><semantics><mrow><mfenced><mrow><mo>−</mo><mi>φ</mi><mfenced><mi>ξ</mi></mfenced></mrow></mfenced></mrow></semantics></math></inline-formula>-Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves Mathematics nonlinear partial differential equations exp(−<i>φ</i>(<i>ξ</i>))-expansion method Heimburg model traveling wave solutions |
| title | Application of the Exp<inline-formula><math display="inline"><semantics><mrow><mfenced><mrow><mo>−</mo><mi>φ</mi><mfenced><mi>ξ</mi></mfenced></mrow></mfenced></mrow></semantics></math></inline-formula>-Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves |
| title_full | Application of the Exp<inline-formula><math display="inline"><semantics><mrow><mfenced><mrow><mo>−</mo><mi>φ</mi><mfenced><mi>ξ</mi></mfenced></mrow></mfenced></mrow></semantics></math></inline-formula>-Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves |
| title_fullStr | Application of the Exp<inline-formula><math display="inline"><semantics><mrow><mfenced><mrow><mo>−</mo><mi>φ</mi><mfenced><mi>ξ</mi></mfenced></mrow></mfenced></mrow></semantics></math></inline-formula>-Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves |
| title_full_unstemmed | Application of the Exp<inline-formula><math display="inline"><semantics><mrow><mfenced><mrow><mo>−</mo><mi>φ</mi><mfenced><mi>ξ</mi></mfenced></mrow></mfenced></mrow></semantics></math></inline-formula>-Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves |
| title_short | Application of the Exp<inline-formula><math display="inline"><semantics><mrow><mfenced><mrow><mo>−</mo><mi>φ</mi><mfenced><mi>ξ</mi></mfenced></mrow></mfenced></mrow></semantics></math></inline-formula>-Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves |
| title_sort | application of the exp inline formula math display inline semantics mrow mfenced mrow mo mo mi φ mi mfenced mi ξ mi mfenced mrow mfenced mrow semantics math inline formula expansion method to find the soliton solutions in biomembranes and nerves |
| topic | nonlinear partial differential equations exp(−<i>φ</i>(<i>ξ</i>))-expansion method Heimburg model traveling wave solutions |
| url | https://www.mdpi.com/2227-7390/10/18/3372 |
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