Abstract
This paper studies the (3+1)-dimensional extended Kadomtsev-Petviashvili equation with power law nonlinearity that apperas in the study of multi-component plasmas. The solutions are obtained by several methods such as modified F-expansion method, exp-function method, G'/G expansion method, ansatz method, traveling wave hypothesis, the improved jacobi's elliptic function method and Lie symmetry analysis. These method lead to several closed form exact solutions. Some of these solutions are topological, non-topological and singular solitons, cnoidal, snoidal waves. It is also shown that in the limiting case, these doubly periodic functions lead to singular periodic functions, complexitons and linear waves. The domain restrictions are also identfified in order for the soliton solutions to exist.