In this paper, we apply the (G /G)-expansion method based on three auxiliary equations, namely, the generalized Riccati equation G (ξ) = r + pG(ξ) + qG 2 (ξ), the Jacobi elliptic equation (G (ξ)) 2 = R + QG 2 (ξ) + PG 4 (ξ) and the second order linear ordinary differential equation (ODE) G (ξ) + λG (ξ) + μG(ξ) = 0 to find many new exact solutions of a nonlinear partial differential equation (PDE) describing the nonlinear low-pass electrical lines. The given nonlinear PDE has been derived and can be reduced to a nonlinear ODE using a simple transformation. Soliton wave solutions, periodic function solutions, rational function solutions and Jacobi elliptic function solutions are obtained. Comparing our new solutions obtained in this paper with the well-known solutions is given. Furthermore, plotting 2D and 3D graphics of the exact solutions is shown.

In this paper, we apply the (G′/G)-expansion method based on three auxiliary equations namely, the generalized Riccati equation, the Jacobi elliptic equation and the second order linear ordinary differential equation to find many new exact solutions of a nonlinear partial differential equation (PDE) describing the nonlinear low-pass electrical lines. The given nonlinear PDE has been derived and can be reduced to a nonlinear ordinary differential equation (ODE) using a simple transformation. Solitons wave solutions, periodic functions solutions, rational functions solutions and Jacobi elliptic functions solutions are obtained. Comparing our new solutions obtained in this paper with the well-known solutions are obtained. The given method in this paper is straightforward, concise and it can also be applied to other nonlinear PDEs in mathematical physics.