New Bäcklund transformations of the (2+1)-dimensional Bogoyavlenskii equation via localization of residual symmetries

The residual symmetry of the (2+1)-dimensional Bogoyavlenskii equation is obtained and localized to a Lie point symmetry by introducing new dependent variables to enlarge the system, then the corresponding finite transformation is obtained by using Lie's first theorem. Furthermore, by introducing more dependent variables, the linear superposition of arbitrary number of residual symmetries is also localized and the corresponding finite transformations which are just Nth Bäcklund transformations of the (2+1)-dimensional Bogoyavlenskii equation are obtained in determinants form with some concrete solutions explicitly given.