# Lie Symmetry Analysis, Analytical Solution, and Conservation Laws of a Sixth-Order Generalized Time-Fractional Sawada-Kotera Equation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Lie Symmetry Analysis

**Definition**

**1**

**.**

## 3. Symmetry Reductions

**Case 1**${X}_{1}=\frac{\partial}{\partial x}$ For ${X}_{1}$, the characteristic equation is

**Case 2**${X}_{2}=x\frac{\partial}{\partial x}+\frac{6t}{\alpha}\frac{\partial}{\partial t}-2u\frac{\partial}{\partial u}$

**Theorem**

**1.**

**Proof.**

## 4. Exact Power Series Solution

## 5. Conservation Laws

**Case 1**For the case in which $\alpha \u03f5(0,1)$,

**Case 2**For the case in which $\alpha \u03f5(1,2)$,

## 6. Concluding Remarks

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

FPDE | Fractional Partial Differential Equation |

IST | Inverse Scattering Transformation |

DT | Darboux Transformation |

EK | Erd$\stackrel{\xb4}{e}$lyi–Kober |

PDE | Partial Differential Equation |

CK | Clarkson–Kruskal |

FPDEs | Fractional Partial Differential Equations |

KdV | Korteweg-de Vries |

RL | Riemann–Liouville |

CLs | Conservation Laws |

CL | Conservation Law |

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**MDPI and ACS Style**

Wang, Y.; Li, L.
Lie Symmetry Analysis, Analytical Solution, and Conservation Laws of a Sixth-Order Generalized Time-Fractional Sawada-Kotera Equation. *Symmetry* **2019**, *11*, 1436.
https://doi.org/10.3390/sym11121436

**AMA Style**

Wang Y, Li L.
Lie Symmetry Analysis, Analytical Solution, and Conservation Laws of a Sixth-Order Generalized Time-Fractional Sawada-Kotera Equation. *Symmetry*. 2019; 11(12):1436.
https://doi.org/10.3390/sym11121436

**Chicago/Turabian Style**

Wang, Yuhang, and Lianzhong Li.
2019. "Lie Symmetry Analysis, Analytical Solution, and Conservation Laws of a Sixth-Order Generalized Time-Fractional Sawada-Kotera Equation" *Symmetry* 11, no. 12: 1436.
https://doi.org/10.3390/sym11121436