LAUSR

Lie group analysis is applied to carry out the similarity reductions of the $$(3+1)$$(3+1)-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation. We obtain generators of infinitesimal transformations of the CBS equation and each of these generators depend on various parameters which give us a set of Lie algebras. For each of these Lie algebras, Lie symmetry method reduces the $$(3+1)$$(3+1)-dimensional CBS equation into a new $$(2+1)$$(2+1)-dimensional partial differential equation and to an ordinary differential equation. In addition, we obtain commutator table of Lie brackets and symmetry groups for the CBS equation. Finally, we obtain closed-form solutions of the CBS equation by using the invariance property of Lie group transformations.