Application of first integral method to some special nonlinear partial differential equations

In this present work, we explore the application of the first integral metho d to some special nonlinear partial differential equations. The power of this manageable method is confirmed by applying it for three selected nonlinear partial differential equations. By using this method, we found some exact solutions of the Tzitzeica-Dodd-Bullough equation and nonlinear Klein-Gordon equation with power law nonlinearity and generalized nonlinear heat conduction equation and the BBM-like B (2, 2) equation. The first integral method can be applied to nonintegrable equations as well as to integrable ones. This method is based on the theory of commutative algebra