Nonlocal symmetry and exact solutions of the (2+1)-dimensional modified Bogoyavlenskii–Schiff equation**Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant

Abstract

In this paper, the truncated Painlevé analysis, nonlocal symmetry, Bäcklund transformation of the (2+1)-dimensional modified Bogoyavlenskii–Schiff equation are presented. Then the nonlocal symmetry is localized to the corresponding nonlocal group by the prolonged system. In addition, the (2+1)-dimensional modified Bogoyavlenskii–Schiff is proved consistent Riccati expansion (CRE) solvable. As a result, the soliton–cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to find by other traditional methods. Moreover figures are given out to show the properties of the explicit analytic interaction solutions.