Lie symmetry analysis and invariant solutions of (3+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{(3+1)}$$\end{document}-dimensional Calogero–Bogoyavlenskii–Schiff equation

Lie group analysis is applied to carry out the similarity reductions of the (3+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(3+1)$$\end{document}-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)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(3+1)$$\end{document}-dimensional CBS equation into a new (2+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(2+1)$$\end{document}-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.