On the modified method of simplest equation and the nonlinear Schrödinger equation

Abstract: We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schr\"odinger equation. It is shown that the methodology works also for other equations of the nonlinear Schr\"odinger kind.