scholarly journals Explicit solution of time fractional modified equal width wave equation by Lie symmetry analysis

2021 ◽  
Keyword(s):  
Wave Equation ◽  
Explicit Solution ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis

scholarly journals Lie Symmetry Analysis and New Exact Solutions for a Higher-Dimensional Shallow Water Wave Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Yinghui He
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Elliptic Function ◽  
Water Wave ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Hyperbolic Function ◽  
Lie Symmetry Analysis ◽  
Shallow Water Wave ◽  
Higher Dimensional

In our work, a higher-dimensional shallow water wave equation, which can be reduced to the potential KdV equation, is discussed. By using the Lie symmetry analysis, all of the geometric vector fields of the equation are obtained; the symmetry reductions are also presented. Some new nonlinear wave solutions, involving differentiable arbitrary functions, expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function, and trigonometric function are obtained. Our work extends pioneer results.

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