Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900738 | Applied Mathematics and Computation | 2018 | 11 Pages |
Abstract
One generalized Burgers hierarchy is derived by applying the Cole-Hopf transforation, whose dark-equation hierarchy is also generated by the dark-equation method, from which a generalized Burgers equation and a generalized Kupershmidt equation, respectively, are followed to obtain. Through Lie-group analysis method we produce similarity reductions, exact solutions of the generalized Burgers and the Kupershmidt equations. Specially, we investigate the similarity reductions of the fractional Kupershmidt equation and its exact solutions. In addition, we obtain the conservation laws of the Kupershmidt equation and its adjoint equation. Finally, we give rise to symmetries, primary branch solutions as well various recursion operators of degenerated equations from the Kupershmidt equation.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Yufeng Zhang, Jianqin Mei, Xiangzhi Zhang,