一个2+1维可积方程的代数几何解

数学物理学报 ›› 2015, Vol. 35 ›› Issue (3): 534-544.

一个2+1维可积方程的代数几何解

陈晓红^1,2, 张大庆¹, 张鸿庆², 尤福财³

1. 辽宁科技大学理学院辽宁鞍山 114051;
2. 大连理工大学数学科学学院辽宁大连 116024;
3. 沈阳工程学院基础教学部沈阳 110136

收稿日期:2013-12-06 修回日期:2014-10-21 出版日期:2015-06-25 发布日期:2015-06-25
通讯作者: 陈晓红, xhchspring@163.com E-mail:xhchspring@163.com
作者简介:张大庆, dq_zhang@163.com;张鸿庆, zhanghq@dlut.edu.cn;尤福财, fcyou2008@yahoo.com.cn
基金资助:
国家自然科学基金(61273011, 11401392)资助

Algebro-Geometric Solutions of A -Dimensional Integrable Equation

Chen Xiaohong^1,2, Zhang Daqing¹, Zhang Hongqing², You Fucai³

1 School of Science, University of Science and Technology LiaoNing, Liaoning Anshan 114051;
2 School of Mathematical Sciences, Dalian University of Technology, Liaoning Dalian 116024;
3 Department of Basic Sciences, Shenyang Institute of Engineering, Shenyang 110136

Received:2013-12-06 Revised:2014-10-21 Online:2015-06-25 Published:2015-06-25

摘要/Abstract

摘要：

该文从 1+1 维的孤子方程出发, 构造出一个2+1维在 Lax 意义下可积的方程. 接着这个 2+1 维可积方程被分解为可解的常微分方程. 随后引入超椭圆 Riemann 曲面和 Abel-Jacobi 坐标把流进行了拉直. 再利用 Riemann θ 函数给出了这个 2+1 维方程的代数几何解.

关键词: 代数几何解, Abel-Jacobi 坐标, Riemann θ 函数

Abstract:

In this paper, a (2+1)-dimensional integrable equation is presented with the help of (1+1)-dimensional soliton equations. The (2+1)-dimensional integrable equation is decomposed into solvable ordinary differential equations. A hyperelliptic Riemann surface and Abel-Jacobi coordinates are introduced to strainghten the associated flow, from which the algebro-geometric solutions of the (2+1)-dimensional integrable equation are constructed by means of the Riemann theta functions.

Key words: Algebro-geometric solution, Abel-Jacobi coordinates, Riemann θ function

中图分类号:

O175.2

陈晓红, 张大庆, 张鸿庆, 尤福财. 一个2+1维可积方程的代数几何解[J]. 数学物理学报, 2015, 35(3): 534-544.

Chen Xiaohong, Zhang Daqing, Zhang Hongqing, You Fucai. Algebro-Geometric Solutions of A -Dimensional Integrable Equation[J]. Acta mathematica scientia,Series A, 2015, 35(3): 534-544.

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