Explicit solution of general fourth order time fractional KdV equation by lie symmetry analysis

2020 ◽  
Author(s):  
H. Gandhi ◽  
D. Singh ◽  
A. Tomar
Keyword(s):  
Fourth Order ◽  
Explicit Solution ◽  
Kdv Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis

Lie symmetry analysis of the deformed KdV equation

2017 ◽  
Vol 31 (30) ◽  
pp. 1750275 ◽  
Author(s):  
Yehui Huang ◽  
Wei Li ◽  
Guo Wang ◽  
Xuelin Yong
Keyword(s):  
Kdv Equation ◽  
Classical Equation ◽  
Analytic Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
System Method ◽  
Exact Analytic Solutions ◽  
Similarity Reductions

The deformed KdV equation is a generalization of the classical equation that can describe the motion of the interaction between different solitary waves. In this paper, the Lie symmetry analysis is performed on the deformed KdV equation. The similarity reductions and exact solutions are obtained based on the optimal system method. The exact analytic solutions are considered by using the power series method. The conservation laws for the deformed KdV equation are presented. Finally, the analytic solutions are given and their dynamics are studied.

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