Painlevé analysis, group invariant analysis, similarity reduction, exact solutions, and conservation laws of Mikhailov–Novikov–Wang equation

Abstract

In this paper, for the study of integrability, symmetry analysis, group invariant solutions and conservation laws, the Mikhailov–Novikov–Wang equation is considered. Firstly, Painlevé analysis is being employed to study the integrability properties for the considered equation so as to check the possibility that this equation passes the Painlevé test. Secondly, Lie group analysis is studied for finding the symmetries by using Lie classical group analysis method and to obtain its symmetry group, infinitesimal generator, Lie algebra commutation table, and similarity reductions. The vector fields and the symmetry reduction of this equation are calculated with the aid of Lie symmetry analysis. From the similarity reduction equation, some explicit exact solutions are derived. Finally, using the new conservation theorem proposed by Ibragimov [N. H. Ibragimov, A new conservation theorem, J. Math. Anal. Appl. 333 (2007) 311–328], the conservation laws of the aforesaid equation have been constructed.