The n-fold Darboux transform (DT) is a 2×2 matrix for the Ablowitz-Kaup-Newell-Segur (AKNS) system.In this paper,each element of this matrix is expressed by 2n + 1 ranks'determinants.Using these formulae,the determinant expressions of eigenfunctions generated by the n-fold DT are obtained.Furthermore,we give out the explicit forms of the n-soliton surface of the Nonlinear Schrodinger Equation (NLS) by the determinant of eigenfunctions.
