Comparison Between Two Methods to Find Exact Solutions for a New Models of Nonlinear Partial Differential Equations

The aim of this paper is to give a connection between two methods, the - expansion method and the tanh method which are used to find exact solutions of nonlinear partial differential equations (NLPDEs). It has been shown that these two methods are the same in special conditions. For illustration we present a new models of Equal-Width (EW) equation and Vaknenko-Parks (VP) equation. Exact traveling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions and rational functions, with the aid of the software Maple.