LAUSR

Abstract In this research, we apply a new technique for solving and obtaining exact and solitary wave solutions of the three dimensional Zakharov–Kuznetsov–Burgers equation for the dust-ion-acoustic waves in dusty plasmas and Boussinesq equation with dual dispersion. We use the improved G ′ G -expansion method with the aid of Maple 16 which support us with three different kinds of solutions (the hyperbolic functions, the trigonometric functions and the rational functions). This method depends on auxiliary equation and also it is considered as one of general method for solving partial differential equations where this method include the extended G ′ G -expansion method when σ = 0 and also the G ′ G -expansion method when N takes only positive value and zero. All of these solutions helps us to investigate the physical meaning of each models and the stability of above mentioned model.