# Variational Principles for Two Kinds of Coupled Nonlinear Equations in Shallow Water

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Variational Principles for the Broer-Kaup Equations

**Proof.**

## 3. Variation Principles for the (2+1)-Dimensional Dispersive Long-Wave Equations

**Proof.**

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Cao, X.-Q.; Guo, Y.-N.; Hou, S.-C.; Zhang, C.-Z.; Peng, K.-C.
Variational Principles for Two Kinds of Coupled Nonlinear Equations in Shallow Water. *Symmetry* **2020**, *12*, 850.
https://doi.org/10.3390/sym12050850

**AMA Style**

Cao X-Q, Guo Y-N, Hou S-C, Zhang C-Z, Peng K-C.
Variational Principles for Two Kinds of Coupled Nonlinear Equations in Shallow Water. *Symmetry*. 2020; 12(5):850.
https://doi.org/10.3390/sym12050850

**Chicago/Turabian Style**

Cao, Xiao-Qun, Ya-Nan Guo, Shi-Cheng Hou, Cheng-Zhuo Zhang, and Ke-Cheng Peng.
2020. "Variational Principles for Two Kinds of Coupled Nonlinear Equations in Shallow Water" *Symmetry* 12, no. 5: 850.
https://doi.org/10.3390/sym12050850