Algebraic traveling wave solutions to nonlinear evolution equations

Abstract

In this paper, we employ planar dynamical systems and invariant algebraic curves to characterize all algebraic traveling wave solutions to nonlinear evolution equations. In order to demonstrate the applicability and efficiency of the method, we apply the approach to four (2+1)-dimensional integrable extensions of the Kadomtsev- Petviashvili equation. The numerical simulations are also plotted for better understanding the physical phenomena.