Determinant representation of Darboux transformation for the AKNS system  

作　　者：HE Jingsong ZHANG Ling CHENG Yi LI Yishen 

机构地区：[1]Department of Mathematics,University of Science and Technology of China,Hefei 230026,China Department of Mathematics,University of Science and Technology of China,Hefei 230026,China Department of Mathematics,University of Science and Technology of China,Hefei 230026,China Department of Mathematics,University of Science and Technology of China,Hefei 230026,China

出　　处：《Science China Mathematics》2006年第12期1867-1878,共12页中国科学：数学（英文版）

基　　金：This work was supported partly by the project 973"Nonlinear Science";the National Natural Science Foundation of China(Grant No.10301030);SRFDP of China.

摘　　要：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.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.

关 键 词：DARBOUX transformation AKNS SYSTEM (Ablowitz-Kaup-Newell-Segur System) determinant soliton surface. 

分 类 号：N[自然科学总论]