Lie symmetry analysis, exact solutions and conservation laws of (3+1)-dimensional modified Wazwaz-Benjamin-Bona-Mahony equation

Abstract In this paper, we study the (3+1)-dimensional modified Wazwaz-Benjamin-Bona-Mahony equation using Lie symmetry analysis. An optimal system is constructed with the help of a commutator table and an adjoint table. Similarity reductions are obtained on the basis of the optimal system, and the governing partial differential equation is transformed into another partial differential equations with a smaller number of independent variables. The solutions of these reduced partial differential equations give invariant solutions of the (3+1)-dimensional modified Wazwaz-Benjamin-Bona-Mahony equation. The 3D graphical plots are used to describe the dynamical characteristics of the solutions. Hence, by employing these graphs, physicists and mathematicians can more efficiently and successfully follow complex physical processes. Finally, self-adjoint is checked, and conservation laws are also deducted corresponding to each infinitesimal generator.