# The Solitary Solutions for the Stochastic Jimbo–Miwa Equation Perturbed by White Noise

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## Abstract

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## 1. Introduction

## 2. Wave Equation for SJM Equation

## 3. Exact Solutions of SJM Equation

#### 3.1. Application of the REM-Method

**Family I:**When $ps>0,$ thus, the solutions of Equation (9) are:

**Family II:**When $ps<0,$ thus the solutions of Equation (9) are:

**Family III:**When $p=0,\phantom{\rule{4pt}{0ex}}s\ne 0,$ then Equation (9) has the solution

#### 3.2. Application of the HSI-Method

## 4. Impacts of Noise

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Al-Askar, F.M.; Cesarano, C.; Mohammed, W.W. The Solitary Solutions for the Stochastic Jimbo–Miwa Equation Perturbed by White Noise. *Symmetry* **2023**, *15*, 1153.
https://doi.org/10.3390/sym15061153

**AMA Style**

Al-Askar FM, Cesarano C, Mohammed WW. The Solitary Solutions for the Stochastic Jimbo–Miwa Equation Perturbed by White Noise. *Symmetry*. 2023; 15(6):1153.
https://doi.org/10.3390/sym15061153

**Chicago/Turabian Style**

Al-Askar, Farah M., Clemente Cesarano, and Wael W. Mohammed. 2023. "The Solitary Solutions for the Stochastic Jimbo–Miwa Equation Perturbed by White Noise" *Symmetry* 15, no. 6: 1153.
https://doi.org/10.3390/sym15061153