N-fold Darboux Transformation for Integrable Couplings of AKNS Equations

被引：0

作者：

虞静 ^{[1
]}

陈守婷 ^{[2
]}

韩敬伟 ^{[3
]}

马文秀 ^{[4
,5
,6
]}

机构：

[1] School of Science Hangzhou Dianzi University

[2] School of Mathematics and Physical Science Xuzhou Institute of Technology

[3] School of Information Engineering Hangzhou Dianzi University

[4] Department of Mathematics and Statistics University of South Florida

[5] College of Mathematics and Systems Science Shandong University of Science and Technology

[6] International Institute for Symmetry Analysis and Mathematical Modeling Department of Mathematical SciencesNorth-West University Mafikeng Campus

来源：

CommunicationsinTheoreticalPhysics | 2018年 / 69卷 / 04期

关键词：

Darboux transformation; integrable couplings of the AKNS equations; determinant representation;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

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.

引用

页码：367 / 374

页数：8