Abstract
In this paper, we discuss one-dimensional optimal system and the invariant solutions of Coupled Burgers’ equations. By using Wu-differential characteristic set algorithm with the aid of Mathematica software, the classical symmetries of the Coupled Burgers’ equations are calculated, and the one-dimensional optimal system of Lie algebra is constructed. And we obtain the invariant solution of the Coupled Burgers’ equations corresponding to one element in one dimensional optimal system by using the invariant method. The results generalize the exact solutions of the Coupled Burgers’ equations.
Highlights
Lie group methods are perhaps the most powerful currently available in finding exact solutions of nonlinear partial differential equations (PDEs) [1]
Not all equations have potential symmetry, because the determining equations (DTEs) of potential symmetry are less than the DTEs of Lie symmetry
Potential symmetry can generate new symmetry and new invariant solutions which could not be obtained by Lie symmetry
Summary
Lie group methods are perhaps the most powerful currently available in finding exact solutions of nonlinear partial differential equations (PDEs) [1]. This method has a profound impact on both pure and applied areas of mathematics, physics and mechanics, etc. 2. The Potential Symmetries, One-Dimensional Optimal System and Lie Transformation Groups of Coupled Burgers’ Equations.
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