lie groups and lie symmetry analysis and travelling wave solutions of equal width wave equation

We can create a deep connection between the world’s industry and technologiesand economic research institutes by using differential equations. we obtained thepower series solution and the travelling wave solutions of equal width wave equationby using the lie symmetry method the fundamental idea behind the symmetry transformationmethod is that it reduces one independent variables in a system of pdesby utilizing lie symmetries and surface invariance condition. we first obtained the infinitesimalsand commutation table with the help of maple software. lie symmetrytransformation method (stm) has been applied on eww equation and converted itinto various nonlinear odes. then, the tanh method and the power series method havebeen applied for solving the reduced nonlinear ordinary differential equations (odes).convergence of the power series solutions has also been shown.