Symmetry properties and explicit solutions of some nonlinear differential and fractional equations

Yufeng Zhang, Jianqin Mei and Xiangzhi Zhang

Applied Mathematics and Computation, 2018, vol. 337, issue C, 408-418

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.

Keywords: Symmetry; Similarity reduction; Conservation law (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:337:y:2018:i:c:p:408-418

DOI: 10.1016/j.amc.2018.05.030

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