#
Application of the Exp$\left(-\phi \left(\xi \right)\right)$ -Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves

^{1}

^{2}

^{3}

^{4}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Heimburg Model Equation

^{2}, assuming a bulk temperature of T = 45 °C [37]. By introducing a dispersive term, we are able to approximate the dispersive effects outlined above, $-h\frac{{\partial}^{4}\u2206{\rho}^{A}}{\partial {z}^{4}}$ with $h>0$, in Equation (1), and we obtain

## 3. Analysis of method

## 4. Application of the Method

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**Three-dimensional, two-dimensional, and contour conspiracies for solution (20) for ${\alpha}_{1}=-0.9,{\beta}_{1}=2,\mu =1,P=0.8,\omega =2,Q=0.8,{a}_{1}=5$.

**Figure 2.**Three-dimensional, two-dimensional, and contour conspiracies for solution (22) for ${\alpha}_{1}=-1.5,{\beta}_{1}=2,\mu =1,\omega =1,Q=1,{a}_{1}=1$.

**Figure 3.**Three-dimensional, two-dimensional, and contour conspiracies for solution (27) ${\alpha}_{1}=-0.9,{\beta}_{1}=2,\omega =1,P=0.8,{a}_{1}=5$.

**Figure 4.**Three-dimensional, two-dimensional, and contour conspiracies for solution (35) for ${\alpha}_{1}=-4,{\beta}_{1}=3,\mu =1,Q=5.6,{a}_{1}=5$.

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**MDPI and ACS Style**

Rani, A.; Shakeel, M.; Kbiri Alaoui, M.; Zidan, A.M.; Shah, N.A.; Junsawang, P.
Application of the Exp*Mathematics* **2022**, *10*, 3372.
https://doi.org/10.3390/math10183372

**AMA Style**

Rani A, Shakeel M, Kbiri Alaoui M, Zidan AM, Shah NA, Junsawang P.
Application of the Exp*Mathematics*. 2022; 10(18):3372.
https://doi.org/10.3390/math10183372

**Chicago/Turabian Style**

Rani, Attia, Muhammad Shakeel, Mohammed Kbiri Alaoui, Ahmed M. Zidan, Nehad Ali Shah, and Prem Junsawang.
2022. "Application of the Exp*Mathematics* 10, no. 18: 3372.
https://doi.org/10.3390/math10183372