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

Abstract Studies on Non-linear evolutionary equations have become more critical as time evolves. Such 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 apply similarity reduction some a (3+1) dimensional nonlinear evolution equation. report, groups symmetries, Tables for commutation, adjoints with infinitesimal generators were established. The subalgebra its optimal system obtained aid adjoint Table. Moreover, equation has been reduced into new PDE having less number independent variables at last ODE, using subalgebras their system, which gives that can represent dynamics waves.