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

摘要

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 ) + qG2(ξ ), the Jacobi elliptic equation(G(ξ ))2 = R + QG2(ξ ) + PG4(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 differentialequation (PDE) describing the nonlinear low-pass electrical lines. The given nonlinearPDE 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 ellipticfunction solutions are obtained. Comparing our new solutions obtained in this paper with thewell-known solutions is given. Furthermore, plotting 2D and 3D graphics of the exact solutionsis shown.