EXPLICIT AND EXACT SOLUTIONS TO NONLINEAR EVOLUTION EQUATIONS VIA THE FIRST INTEGRAL METHOD

In this paper, we show the applicability of the first integral method for obtaining exact solutions of 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 double combined sinh-cosh-Gordon equation and the derivative nonlinear Schr¨odinger equation and the BKdV(n,1) 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.