Lie symmetry analysis, optimal system, and new exact solutions of a (3 + 1) dimensional nonlinear evolution equation

Studies on Non-linear evolutionary equations have become more critical as time evolves. Such equations are not far-fetched in fluid mechanics, plasma physics, optical fibers, and other scientific applications. It should be an essential aim to find exact solutions of these equations. In this work, the Lie group theory is used to apply the similarity reduction and to find some exact solutions of a (3+1) dimensional nonlinear evolution equation. In this report, the groups of symmetries, Tables for commutation, and adjoints with infinitesimal generators were established. The subalgebra and its optimal system is obtained with the aid of the adjoint Table. Moreover, the equation has been reduced into a new PDE having less number of independent variables and at last into an ODE, using subalgebras and their optimal system, which gives similarity solutions that can represent the dynamics of nonlinear waves.