Abstract
In this paper, we study the well known Zakhrov equation (ZE) which states to the Langmuir waves propagation in the ionized plasma. The exact soliton solutions of ZE are extracted using new extended direct algebraic method (EDAM). The obtained solutions are given in the form of trigonometric, rational and hyperbolic functions. Moreover, some of the obtained solutions are illustrated graphically to establish the physical nature of the selected solutions. The existence of these exact solutions is guaranteed by the constraints on the used parameters. It is noted that the new EDAM is easy and efficient technique and it can be useful to many other non-linear partial differential equations (PDEs).