摘要
For the integrable couplings of Ablowitz-Kaup-Newell-Segur(ICAKNS) equations, N-fold Darboux transformation(DT) TN, which is a 4 × 4 matrix, is constructed in this paper. Each element of this matrix is expressed by a ratio of the(4N + 1)-order determinant and 4N-order determinant of eigenfunctions. By making use of these formulae,the determinant expressions of N-transformed new solutions p^([N ]), q^([N ]), r^([N ])and s^([N ])are generated by this N-fold DT.Furthermore, when the reduced conditions q =-p*and s =-r*are chosen, we obtain determinant representations of N-fold DT and N-transformed solutions for the integrable couplings of nonlinear Schr?dinger(ICNLS) equations.Starting from the zero seed solutions, one-soliton solutions are explicitly given as an example.
作者
Jing Yu
Shou-Ting Chen
Jing-Wei Han
Wen-Xiu Ma
虞静;陈守婷;韩敬伟;马文秀(School of Science, Hangzhou Dianzi University, Hangzhou 310018, China;School of Mathematics and Physical Science, Xuzhou Institute of Technology, Xuzhou 221111, China;School of Information Engineering, Hangzhou Dianzi University, Hangzhou 310018, China;Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA;College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;International Institute for Symmetry Analysis and Mathematical Modeling, Department of Mathematical Sciences North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa)
基金
Supported by the National Natural Science Foundation of China under Grant Nos.61771174,11371326,11371361,11301454,and11271168
Natural Science Fund for Colleges and Universities of Jiangsu Province of China under Grant No.17KJB110020
General Research Project of Department of Education of Zhejiang Province(Y201636538)
