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In this paper, we apply the (G′/G)-expansion method based on three auxiliary equations, namely, the generalized Riccati equation G ′ (ξ) = r + p G (ξ) + q G 2 (ξ) , the Jacobi elliptic equation (G ′ (ξ)) 2 = R + Q G 2 (ξ) + P G 4 (ξ) and the second order linear ordinary differential equation (ODE) G ′′ (ξ) + λ G ′ (ξ) + μ G (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. [ABSTRACT FROM AUTHOR]

In this article, we apply the two variable G′G,1G-expansion method with the aid of symbolic computation to construct many new exact solutions for two higher-order nonlinear partial differential equatuions (PDEs) namely, the higher-order nonlinear Schrö dinger (NLS) equation with derivative non-kerr nonlinear terms describing pulse of the propagation beyond ultrashort range in optical communication systems and the higher-order nonlinear quantum Zakharov-Kuznetsov (QZK) equation which arises in quantum magneto plasma. Also, based on Liénard equation, we find many other diffrent new soliton solutions of the above NLS equation. Soliton solutions, periodic solutions, rational functions solutions and Jacobi elliptic functions solutions are obtained. Comparing our new solutions obtained in this article with the well-known solutions are given. [ABSTRACT FROM AUTHOR]