与薛丁谔型谱问题相联系的孤子族的分解

数学季刊 ›› 2008, Vol. 23 ›› Issue (3): 453-457.

与薛丁谔型谱问题相联系的孤子族的分解

1. Department of Mathematics,Zhoukou Normal University 2. Department of Mathematics,Zhengzhou University

收稿日期:2007-11-05 出版日期:2008-09-30 发布日期:2023-09-25
作者简介: XING Xiu-zhi(1969- ), female, native of Dancheng, Henan, an associate professor of Zhoukou Normal University, M.S.D., engages in finite-dimensional integrable system.
基金资助:
Supported by the Youth Fund of Zhoukou Normal University(ZKnuqn200606)

Decomposition of Soliton Hierarchy Associated with a Schroinger Type Spectral Problem

1. Department of Mathematics,Zhoukou Normal University 2. Department of Mathematics,Zhengzhou University

Received:2007-11-05 Online:2008-09-30 Published:2023-09-25
About author: XING Xiu-zhi(1969- ), female, native of Dancheng, Henan, an associate professor of Zhoukou Normal University, M.S.D., engages in finite-dimensional integrable system.
Supported by:
Supported by the Youth Fund of Zhoukou Normal University(ZKnuqn200606)

摘要/Abstract

摘要： The soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems by using the nonlinearized approach. It is worth to point that the solutions for the soliton hierarchy are reduced to solving the compatible Hamiltonian systems of ordinary differential equations.

关键词: soliton hierarchy, spectral problem, Hamiltonian system

Abstract: The soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems by using the nonlinearized approach. It is worth to point that the solutions for the soliton hierarchy are reduced to solving the compatible Hamiltonian systems of ordinary differential equations.

Key words: soliton hierarchy, spectral problem, Hamiltonian system

中图分类号:

O175.9

邢秀芝, 吴景珠, 耿献国. 与薛丁谔型谱问题相联系的孤子族的分解[J]. 数学季刊, 2008, 23(3): 453-457.

XING Xiu-zhi , WU Jing-zhu, GENG Xian-guo. Decomposition of Soliton Hierarchy Associated with a Schroinger Type Spectral Problem [J]. Chinese Quarterly Journal of Mathematics, 2008, 23(3): 453-457.

[1]	魏含玉, 郭汉东, 夏铁成. 与一族（1+1）维孤子方程相联系的有限维可积系[J]. 数学季刊, 2015, 30(4): 503-514.
[2]	周宏宪, 张燕. 一类Z₂-等变扰动的三次哈密顿系统极限环的个数与分布[J]. 数学季刊, 2011, 26(1): 144-151.
[3]	邢秀芝, 吴景珠, 耿献国. 一族与薛定谔型谱问题相联系的新的孤子方程及其相应的有限维可积系统[J]. 数学季刊, 2006, 21(2): 220-228.
[4]	徐新生, 张洪武, 钟万勰. A Direct Method for the Problem of the Solid Cylinder in Elasticity[J]. 数学季刊, 1998, 13(1): 44-54.