Dbar Dressing Method To The Focusing Nonlinear Schr?dinger Equation With Nonzero Boundary Conditions

The Dbar-dressing method based on the local(?)(Dbar)-problem is generalized to study the focusing nonlinear Schrodinger equation,with nonzero boundary conditions.The Lax pair of the focusing nonlinear Schrodinger equation with nonzero boundary conditions are constructed first.Then,the N-soliton solution of the focusing nonlinear Schrodinger equation with nonzero boundary conditions are derived by virtue of choosing the special spectral transformation matrix.Moreover,the one-soliton solution of the focusing nonlinear Schrodinger equation with nonzero boundary conditions are obtained.