The (G′/G)-expansion method for solving a nonlinear PDE describing the nonlinear low-pass electrical lines

Abstract

In this paper, we apply the (G′/G)-expansion method based on three auxiliary equations, namely, the generalized Riccati equation (Formula presented.), the Jacobi elliptic equation (Formula presented.) and the second order linear ordinary differential equation (ODE) (Formula presented.) 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.