The First Integral Method for the Generalized Drinfel’d–Sokolov–Wilson system and Bretherton equation

First integral method, which is called also FIM, in short, is usually applied to nonlinear partial differential equations. This method usually leads to an exact solution. This manuscript, the first integral method is applied to find exact Solitons solutions of the generalized forms of Drinfel’d–Sokolov–Wilson system, and Bretherton equation. FIM is based on the theory of commutative algebra.