Invariant analysis, optimal system of Lie sub-algebra and conservation laws of (3+1)-dimensional KdV–BBM equation

Abstract

In this paper, a nonlinear fourth-order (3+1)-dimensional KdV Benjamin–Bona–Mahony equation is studied using Lie symmetry approach. Lie symmetry analysis is executed to obtain the entire vector field, group-invariant solutions and similarity reductions based on the one-dimensional optimal sub-algebra. One-dimensional optimal systems are constructed using adjoint representation of a Lie group on its Lie algebra. Finally, the conservation laws have been obtained by considering the “new conservation theorem” proposed by Ibragimov.