Abstract
In the present paper, we mainly focus on the symmetry of the solutions of a given PDE via Lie group method. Meanwhile we transfer the given PDE to ODEs by making use of similarity reductions. Furthermore, it is shown that the given PDE is self-adjoining, and we also study the conservation law via multiplier approach.
Highlights
On the contribution of the Lie symmetry method, significant studies have been performed on the integrability of the nonlinear partial differential equation (PDE), group classification, optimal system, reduced solutions and conservation laws, such as [11,12,13,14,15,16,17,18,19,20,21,22,23], and references therein
The Lie symmetry and similarity reductions and the soliton solutions can be researched in the near future
The vector fields which make the equation under consideration symmetry are obtained
Summary
On the contribution of the Lie symmetry method, significant studies have been performed on the integrability of the nonlinear PDEs, group classification, optimal system, reduced solutions and conservation laws, such as [11,12,13,14,15,16,17,18,19,20,21,22,23], and references therein. (1) For the generator V1 , we assume ζ = t, u = f (ζ ) and obtain the trivial solution f = c, where c is an arbitrary nonzero constant. By substituting (27) into Equation (2), we get the trivial solution f = c, where c is an arbitrary nonzero constant.
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