Abstract
The generalized Kadomtsive–Petviashvili modified equal width-Burgers (KP-MEW-B) equation described the propagation of long-wave with dissipation and dispersion in nonlinear media. We investigated the solitary wave solutions of generalized KP-MEW-B equation by applying modification form of extended auxiliary equation mapping method. As a results, families of solitary wave solutions are obtained in different form of solitons: the single bright–dark solitons, the double bright–dark solitons and traveling wave solutions. The physical structure of these new solutions are shown in two and three dimensional graphically with the aid of computer software Mathematica. These obtained new solutions show the power and effectiveness of this new method. We can also solve other unstable nonlinear system of PDEs which are involved in mathematical physics and many other branches of physical sciences with the help of this new method .