Abstract
In this research, we study new two techniques that called the extended simple equation method and the novel (G '/G)-expansion method. The extended simple equation method depend on the auxiliary equation (d phi/d xi = alpha + lambda phi + mu phi(2)) which has three ways for solving depends on the specific condition on the parameters as follow: When (lambda = 0) this auxiliary equation reduces to Riccati equation, when (alpha = 0) this auxiliary equation reduces to Bernoulli equation and when (alpha not equal 0, lambda not equal 0, mu not equal 0) we the general solutions of this auxiliary equation while the novel (G '/G)-expansion method depends also on similar auxiliary equation ((G '/G)' = mu + lambda(G '/G) + (nu - 1)(G '/G)(2)) which depend also on the value of (lambda(2) = 4(nu - 1)mu) and the specific condition on the parameters as follow: When (lambda = 0) this auxiliary equation reduces to Riccati equation, when (mu = 0) this auxiliary equation reduces to Bernoulli equation and when (lambda(2) not equal 4(nu - 1)mu) we the general solutions of this auxiliary equation. This show how both of these auxiliary equation are special cases of Riccati equation. We apply these methods on two dimensional nonlinear Kadomtsev-Petviashvili Burgers equation in quantum plasma and three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. We obtain the exact traveling wave solutions of these important models and under special condition on the parameters, we get solitary traveling wave solutions. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions. (C) 2018 The Author. Published by Elsevier B.V.