对偶薛定谔方程族与导数薛定谔方程族的对应关系  

The Correspondence between the Dual NLS Hierarchy and the Derivative NLS Hierarchy

作　　者：郭明月 康婷 王云波 GUO Mingyue;KANG Ting;WANG Yunbo(School of Mathematices,Northwest University,Xi'an 710127;Center for Nonlinear Studies,Northwest University,Xi'an 710069)

机构地区：[1]西北大学数学学院,西安710127 [2]西北大学非线性科学研究中心,西安710069

出　　处：《工程数学学报》2021年第5期691-699,共9页Chinese Journal of Engineering Mathematics

基　　金：陕西省自然科学基金(2019JC-28).

摘　　要：本文主要研究对偶薛定谔方程族与导数薛定谔方程族及其守恒律之间的对应关系.第一部分,我们根据导数薛定谔方程与对偶薛定谔方程之间的规范变换的形式,给出这两个方程族递推算子之间的一一对应,并在此基础上证明了导数薛定谔方程与对偶薛定谔方程之间的规范变换也为这两个方程族之间的一一对应.第二部分,我们根据第一部分两方程族之间一一对应的形式,给出了这两个方程族哈密顿泛函变分导数之间的一一对应,进而得到了两方程族哈密顿守恒律之间的一一对应.In this paper,we study the one-to-one correspondence between the dual NLS hierarchy and derivative NLS hierarchy,and associated Hamiltonian conservation laws.The first part,we give the correspondence between these two recursion operators according to the gauge transformation between the dual NLS and derivative NLS equations.And base on these relationships,we prove that these two equation hierarchies have the same gauge transformation.The sencond part,we propose the correspondence between these two equation hierarchies about the variation derivative of Hamiltonian functional.And then,we obtain to the relationship about their associated Hamiltonian conservation laws.

关 键 词：规范变换 三哈密顿对偶 递推算子 哈密顿守恒律 

分 类 号：O175.29[理学—数学]