# Investigation into the Explicit Solutions of the Integrable (2+1)—Dimensional Maccari System via the Variational Approach

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The VP

_{1}, γ

_{2}, γ

_{3}, ε

_{1}, ε

_{2}and ε

_{3}are arbitrary constants.

## 3. The PWSs

**Note:**We can also obtain the other different PWSs via supposing $p\left(\xi \right)=\mathrm{\Lambda}\mathrm{sin}\left(\varpi \xi \right)$, $p\left(\xi \right)=\mathrm{\Lambda}{\mathrm{cos}}^{2}\left(\varpi \xi \right)$ and so on.

## 4. The SWSs

**Family one:**

**Family two:**

## 5. Numerical Results and Discussion

_{1}= −1, γ

_{2}= 1, γ

_{3}= 1, ε

_{1}= 1, ε

_{2}= 1, ε

_{3}= 1.

**Family one:**

**Family two:**

## 6. Conclusions and Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The AP, RP and IP of the PWS given by Equation (42) at t = 1. (

**A**) The performance of $p\left(x,y,t\right)$. (

**Aa**) The 3-D plot and density contour of the AP. (

**Ab**) The 3-D plot and density contour of the RP. (

**Ac**) The 3-D plot and density contour of the IP. (

**B**) The performance of $q\left(x,y,t\right)$. (

**Ba**) The 3-D plot and density contour of the AP. (

**Bb**) The 3-D plot and density contour of the RP. (

**Bc**) The 3-D plot and density contour of the IP.

**Figure 2.**The AP, RP and IP of the SWS given by Equation (43) at t = 2. (

**A**) The performance of $p\left(x,y,t\right)$. (

**Aa**) The 3-D plot and density contour of the AP. (

**Ab**) The 3-D plot and density contour of the RP. (

**Ac**) The 3-D plot and density contour of the IP. (

**B**) The performance of $q\left(x,y,t\right)$. (

**Ba**) The 3-D plot and density contour of the AP. (

**Bb**) The 3-D plot and density contour of the RP. (

**Bc**) The 3-D plot and density contour of the IP.

**Figure 3.**The AP, RP and IP of the SWS given by Equation (44) at t = 2. (

**A**) The performance of $p\left(x,y,t\right)$. (

**Aa**) The 3-D plot and density contour of the AP. (

**Ab**) The 3-D plot and density contour of the RP. (

**Ac**) The 3-D plot and density contour of the IP. (

**B**) The performance of $q\left(x,y,t\right)$. (

**Ba**) The 3-D plot and density contour of the AP. (

**Bb**) The 3-D plot and density contour of the RP. (

**Bc**) The 3-D plot and density contour of the IP.

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Wang, K.-J.; Si, J.
Investigation into the Explicit Solutions of the Integrable (2+1)—Dimensional Maccari System via the Variational Approach. *Axioms* **2022**, *11*, 234.
https://doi.org/10.3390/axioms11050234

**AMA Style**

Wang K-J, Si J.
Investigation into the Explicit Solutions of the Integrable (2+1)—Dimensional Maccari System via the Variational Approach. *Axioms*. 2022; 11(5):234.
https://doi.org/10.3390/axioms11050234

**Chicago/Turabian Style**

Wang, Kang-Jia, and Jing Si.
2022. "Investigation into the Explicit Solutions of the Integrable (2+1)—Dimensional Maccari System via the Variational Approach" *Axioms* 11, no. 5: 234.
https://doi.org/10.3390/axioms11050234