The solutions q[n] generated from a periodic ＂seed＂ q = cei（as＋bt） of t：he nonlinear SchrS- dinger （NLS） by n-fold Darboux transformation is represented by determinant. Furthermore, the s-periodic solution and t-periodic solution are given explicitly by using q[1]. The curves and surfaces （F1, F2, F3） associated with q[n] are given by means of Sym formula. Meanwhile, we show periodic and asymptotic properties of these curves.
