Surfaces and Curves Corresponding to the Solutions Generated from Periodic“Seed”of NLS Equation  

作　　者：Ling ZHANG Jing Song HE Yi CHENG Yi Shen LI 

机构地区：[1]Department of Mathematics,University of Science and Technology of China [2]Department of Mathematics,Chuzhou University [3]Department of Mathematics,Ningbo University

出　　处：《Acta Mathematica Sinica,English Series》2012年第8期1713-1726,共14页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.10971109);Program for New Century Excellent Talents in University(Grant No.NCET-08-0515);Natural Science Foundation of Anhui Province(Grant Nos.KJ2007B024,KJ2011Z287)

摘　　要：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.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.

关 键 词：Darboux transformation nonlinear SchrSdinger equation integrable surface 

分 类 号：O186.11[理学—数学] TP391.41[理学—基础数学]