Exact solutions for some differential equations through different methods

In this thesis, we will study the nonlinear partial differential equations such as, the extended quantum Zakhrov-Kuznetsov equation, the Gilson-Pickering equation, the system of equations for the ion sound and Langmuir waves, and some other nonlinear partial differential equations by different methods. We will present new results of the mentioned models in the literature. In addition, we will modified the new method namely, the modified generalized exponential rational function method, study some nonlinear partial differential equation, implement newly modified method to some nonlinear partial differential equation. Study modulation instability analysis, and applications of some powerful methods to the nonlinear partial differential equation.