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论文类型：期刊论文

发表时间：2018-11-15

发表刊物：APPLIED MATHEMATICS AND COMPUTATION

收录刊物：SCIE、Scopus

卷号：337

页面范围：408-418

ISSN号：0096-3003

关键字：Symmetry; Similarity reduction; Conservation law

摘要：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.