Abstract
This paper studies the solution of the Kadomtsev-Petviasvili equation with power law nonlinearity in 1+3 dimensions. The Lie symmetry approach as well as the extended tanh-function and G'/G methods are used to carry out the analysis. Subsequently, the soliton solution is obtained for this equation with power law nonlinearity. Both topological as well as non-topological solitons are obtained for this equation. Copyright (C) 2010 John Wiley & Sons, Ltd.