On the similarity reduction solutions of the Bogoyavlenskii equation

In the present paper, we attempt to investigate the nonlocal symmetries and similarity reduction solutions for the Bogoyavlenskii equation. The nonlocal symmetries are obtained by the truncated Painleve expansion and localized to a prolonged system by introducing four auxiliary variables. Then we construct two types similarity reduction solutions. It is observed that some interesting soliton-cnoidal wave solutions can be generated. We further discuss their asymptotic behaviors both in analytical and in graphical ways. (c) 2022 Elsevier Ltd. All rights reserved.