Determinant representation of Darboux transformation for the AKNS system

Abstract

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.