基于约束流的Kaup-Newell方程的Darboux变换的非线性化

Nonlinearizations of Darboux transformations of Kaup-Newell equation based on the restricted Kaup-Newell flow

本文研究Kaup-Newell方程的Darboux变换的非线性化.基于Kaup-Newell方程的Darboux变换经过非线性化得到的映射是约束Kaup-Newell流的Bcklund变换的假设,本文获得了Darboux矩阵中的位势与特征函数之间的约束,由此实现了Kaup-Newell方程的Darboux变换的非线性化,生成了4个具有相同不变量的可积辛映射.

Nonlinearizations of Darboux transformations of Kaup-Newell equation are investigated. Based on the assumption that the maps obtained by nonlinearizing of Darboux transformations of Kaup-Newell equation are just the Backlund transformations of the restricted Kaup-Newell flows, constraints between the potentials in the Darboux matrices and the eigenfunctions can be simply established. Nonlinearizations of four fundamen- tal Darboux transformations are carried out and four integrable symplectic maps which share the same set of invariants are obtained.