Journal of Taibah University for Science (Dec 2019)
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 $ G^{\prime}(\xi ) = r + pG(\xi ) + q{G^2}(\xi ) $ , the Jacobi elliptic equation $ {({G^{\prime}(\xi )} )^2} = R + Q{G^2}(\xi ) + P{G^4}(\xi ) $ and the second order linear ordinary differential equation (ODE) $ G^{\prime\prime}(\xi ) + \lambda G^{\prime}(\xi ) + \mu G(\xi ) = 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.
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