Abstract: New exact solutions of some important nonlinear partial differential equations in one and two dimensions are obtained by using the direct algebraic method. The applicability of the method is demonstrated by applying it for the equal width wave (EW) equation, modified equal width wave (MEW) equation, improved Korteweg de Vries (IKdV) equation, modified regularized long wave (MRLW) equa...

It is shown that solitary-wave solutions of model equations for long waves have an analytic extension to a strip in the complex plane that is symmetric about the real axis. The classes of equations to which the analysis applies include equations of Korteweg-de Vries type, the regularized long wave equations, as well as particular instances of nonlinear Schrr odinger equations.