广义Kaup-Newell方程的Hamilton结构及其代数几何解

魏含玉, 皮国梅

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

数学季刊 >

2019 , Vol. 34 >Issue 2: 209 - 220

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2019.02.009

广义Kaup-Newell方程的Hamilton结构及其代数几何解

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

WEI Han-yu(1982-), male, native of Zhoukou, Henan, associate professor of Zhoukou Normal University, Ph.D., engages in solitons and integrable systems.

录用日期: 2017-08-02

网络出版日期: 2020-10-06

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)；

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

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

WEI Han-yu(1982-), male, native of Zhoukou, Henan, associate professor of Zhoukou Normal University, Ph.D., engages in solitons and integrable systems.

Accepted date: 2017-08-02

Online published: 2020-10-06

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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

本文引用格式

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

Abstract

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

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