In this study we propose a mathematical model in a form of nonlinear partial differential equations (NPDEs) to describe the spatio-temporal dynamics of interacting populations incorporating nonlocal effects and long range diffusion. We are interested in the particular case of one population migrating in one spatial direction. Then the generalized model is reduced to one NPDE of diffusion-advection-reaction kind. We extract a general analytical solution of the considered equation applying a particular variant of Simple Equations Method (SEsM). Several particular solutions are also derived by using different types of the simple equation. Numerical study of the obtained solutions is made as it is shown that the population density wave can vary in its profile depending on the numerical values of a key model parameter.