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Indexed by:期刊论文

Date of Publication:2018-11-15

Journal:APPLIED MATHEMATICS AND COMPUTATION

Included Journals:SCIE、Scopus

Volume:337

Page Number:408-418

ISSN No.:0096-3003

Key Words:Symmetry; Similarity reduction; Conservation law

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. (C) 2018 Elsevier Inc. All rights reserved.