Extended Fan's Algebraic Method and Its Applicationto KdV and Variant Boussinesq Equations

An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinear partial differential equations. The key idea of this method is to introduce an auxiliary ordinary differential equation which is regarded as an extended elliptic equation andwhose degree r is expanded to the case of r>4. The efficiency of themethod is demonstrated by the KdV equation and the variant Boussinesqequations. The results indicate that the method not only offers allsolutions obtained by using Fu's and Fan's methods, but also some new solutions.