# Soliton Solutions of Mathematical Physics Models Using the Exponential Function Technique

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## Abstract

**:**

## 1. Introduction

## 2. Groundwork for Conformable Derivative

**Theorem**

**1.**

## 3. Presentation of Exp-Function Method for Nonlinear Conformable Pdes

## 4. Exact Solutions of Burger’S Equation, $Zk$ Equation and Kdv Equation

#### 4.1. Exact Solutions of Conformable $Zk$ Equation

#### 4.2. Exact Solution of Conformable Kdv Equation

#### 4.3. Exact Solution of Conformable Burgers Equation

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The 3D solution in pictorial form for the function $u(x,y,t)$, and for the parameter values $p=q=t=1.0$ and $\zeta =0.50$.

**Figure 2.**The 3D solution in pictorial form for the function $u(x,y,t)$, and for the parameter values $p=q=t=1.0$ and $\zeta =0.75$.

**Figure 3.**The 3D solution in pictorial form for the function $u(x,y,t)$, and for the parameter values $p=q=t=1.0$ and $\zeta =1.00$.

**Figure 4.**2D and 3D solutions in pictorial form for function $u(x,y,t)$, for the parameter values $p=q=t=1.0$ and $\zeta =0.25,\zeta =0.50,\zeta =0.75,\zeta =1.00$

**Figure 5.**3D solution in the pictorial form for the function $u(x,t)$ for $\gamma =\beta =p=1.00$ and for $\zeta =0.50$.

**Figure 6.**3D solution in the pictorial form for the function $u(x,t)$ for $\gamma =\beta =p=1.00$ and for $\zeta =0.75$.

**Figure 7.**3D solution in pictorial form for the function $u(x,t)$ for $\gamma =\beta =p=1.00$ and for $\zeta =1.00$.

**Figure 8.**2D and 3D solutions in the pictorial form for the function $u(x,t)$ and for various values of $\zeta $.

**Figure 12.**Graphs of the function $u(x,t)$ for the values $\nu =2.0$ and for various values of $\zeta .$

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**MDPI and ACS Style**

Javeed, S.; Saleem Alimgeer, K.; Nawaz, S.; Waheed, A.; Suleman, M.; Baleanu, D.; Atif, M.
Soliton Solutions of Mathematical Physics Models Using the Exponential Function Technique. *Symmetry* **2020**, *12*, 176.
https://doi.org/10.3390/sym12010176

**AMA Style**

Javeed S, Saleem Alimgeer K, Nawaz S, Waheed A, Suleman M, Baleanu D, Atif M.
Soliton Solutions of Mathematical Physics Models Using the Exponential Function Technique. *Symmetry*. 2020; 12(1):176.
https://doi.org/10.3390/sym12010176

**Chicago/Turabian Style**

Javeed, Shumaila, Khurram Saleem Alimgeer, Sidra Nawaz, Asif Waheed, Muhammad Suleman, Dumitru Baleanu, and M. Atif.
2020. "Soliton Solutions of Mathematical Physics Models Using the Exponential Function Technique" *Symmetry* 12, no. 1: 176.
https://doi.org/10.3390/sym12010176