A direct algebraic method applied to obtain complex solutions of some nonlinear partial differential equations

By using some exact solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the NLS equation, a new Hamiltonian amplitude equation, the coupled Schrodinger–KdV equations and the Hirota–Maccari equations. New exact complex solutions are obtained.