In this research, we construct the traveling wave solutions for some nonlinear evolution equations in mathematical physics. New solutions such as soliton solutions are found. The method used is the generalized Kudryashov method (GKM). We apply the method successfully to find the exact solutions of the following nonlinear integro-partial differential equations: the (1 + 1)-dimensional integro-differential Ito equation, (2 + 1)-dimensional integro-differential Sawada–Kotera equation and two members of integrodifferential Kadomtsev–Petviashvili (KP) hierarchy equations. These equations have numerous important applications in mathematical physics as well as in engineering. This method is efficient, powerful and simple