Nonlinear Schrdinger equation for deep-water wave and its exact solutions

Debnath derived the nonlinear schr dinger(NLS)equation form from the general form of the nonlinear wave dispersion relation.In this paper,the analysis of the NLS equation bagins from the 2-order Stokes' nonlinear deep-water wave dispersion relation.The exact solutions of the nonlinear wave are obtained by using the modified mapping method.As this specialization of this equation,the solutions are different from those that obtain and contain the solutions as Debnath did.At the same time,the solitary solution is obtained in the their limit.