In this paper, we establish exact solutions for some special nonlinear partial differential equations. The ($G'/G$)-expansion method is used to construct travelling wave solutions of the twodimensional sine-Gordon equation, Dodd–Bullough–Mikhailov and Schrödinger–KdV equations, which appear in many fields such as, solid-state physics, nonlinear optics, fluid dynamics, fluid flow, quantum field theory, electromagnetic waves and so on. In this method we take the advantage of general solutions of second-order linear ordinary differential equation (LODE) to solve many nonlinear evolution equations effectively. The ($G'/G$)-expansion method is direct, concise and elementary and can be used with a wider applicability for handling many nonlinear wave equations.