广义Kaup-Newell方程的Hamilton结构及其代数几何解

doi:10.13371/j.cnki.chin.q.j.m.2019.02.009

数学季刊 ›› 2019, Vol. 34 ›› Issue (2): 209-220.doi: 10.13371/j.cnki.chin.q.j.m.2019.02.009

• • 上一篇

广义Kaup-Newell方程的Hamilton结构及其代数几何解

College of mathematics and statistics,Zhoukou Normal UniversityCollege of Economics and Management,Zhoukou Normal University

接受日期:2017-08-02 出版日期:2019-06-30 发布日期:2020-10-06
作者简介:WEI Han-yu(1982-), male, native of Zhoukou, Henan, associate professor of Zhoukou Normal University, Ph.D., engages in solitons and integrable systems.
基金资助:
Supported by the Natural Science Foundation of China(Grant Nos.11547175,11271008)； Supported by the Science and Technology Department of Henan Province(No.182102310978)； Supported by the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education of China(Grant Nos.2017GGJS145,2014GGJS-195)；

The Hamiltonian Structures and Algebro-geometric Solution of the Generalized Kaup-Newell Soliton Equations

College of mathematics and statistics,Zhoukou Normal UniversityCollege of Economics and Management,Zhoukou Normal University

Accepted:2017-08-02 Online:2019-06-30 Published:2020-10-06
About author:WEI Han-yu(1982-), male, native of Zhoukou, Henan, associate professor of Zhoukou Normal University, Ph.D., engages in solitons and integrable systems.
Supported by:
Supported by the Natural Science Foundation of China(Grant Nos.11547175,11271008)； Supported by the Science and Technology Department of Henan Province(No.182102310978)； Supported by the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education of China(Grant Nos.2017GGJS145,2014GGJS-195)；

摘要/Abstract

摘要： Staring from a new spectral problem, a hierarchy of the generalized Kaup-Newell soliton equations is derived. By employing the trace identity their Hamiltonian structures are also generated. Then, the generalized Kaup-Newell soliton equations are decomposed into two systems of ordinary differential equations. The Abel-Jacobi coordinates are introduced to straighten the flows, from which the algebro-geometric solutions of the generalized KaupNewell soliton equations are obtained in terms of the Riemann theta functions.

关键词: Soliton equations, Hamiltonian structures, Algebro-geometric solutions, Riemann theta functions

Abstract: Staring from a new spectral problem, a hierarchy of the generalized Kaup-Newell soliton equations is derived. By employing the trace identity their Hamiltonian structures are also generated. Then, the generalized Kaup-Newell soliton equations are decomposed into two systems of ordinary differential equations. The Abel-Jacobi coordinates are introduced to straighten the flows, from which the algebro-geometric solutions of the generalized KaupNewell soliton equations are obtained in terms of the Riemann theta functions.

Key words: Soliton equations, Hamiltonian structures, Algebro-geometric solutions, Riemann theta functions

中图分类号:

O175

魏含玉, 皮国梅. 广义Kaup-Newell方程的Hamilton结构及其代数几何解[J]. 数学季刊, 2019, 34(2): 209-220.

WEI Han-yu, PI Guo-mei. The Hamiltonian Structures and Algebro-geometric Solution of the Generalized Kaup-Newell Soliton Equations[J]. Chinese Quarterly Journal of Mathematics, 2019, 34(2): 209-220.

广义Kaup-Newell方程的Hamilton结构及其代数几何解

The Hamiltonian Structures and Algebro-geometric Solution of the Generalized Kaup-Newell Soliton Equations

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

编辑推荐

Metrics

本文评价