Lie symmetry analysis and exact solutions of (3+1) dimensional Yu-Toda-Sasa-Fukuyama equation in mathematical physics

In this paper, the Lie symmetry analysis method has been proposed for finding similarity reduction and exact solutions of nonlinear evolution equation. Here for illustrating the effectiveness and accuracy of proposed method, we have taken (3+1) dimensional Yu-Toda-Sasa-Fukuyama (YTFS) equation. Also by using symmetry reduction method, we have reduced nonlinear partial differential equation (NPDE) to nonlinear ordinary differential equation, which has advantage to provide semi analytical solution. We have obtained infinitesimal generators, the entire geometric vector field, commutator table of Lie algebra and symmetry group by using Lie symmetry analysis method. Then, we have used tanh method for finding new analytical exact solutions of some reduced transform equations.