A novel hierarchy of differential-integral equations and their generalized bi-Hamiltonian structures

With the aid of the zero-curvature equation, a novel integrable hierarchy of nonlinear evolution equations associated with a 3 x 3 matrix spectral problem is proposed. By using the trace identity, the bi-Hamiltonian structures of the hierarchy are established with two skew-symmetric operators. Based...

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Bibliographic Details
Published inChinese physics B Vol. 23; no. 6; pp. 13 - 17
Main Author 翟云云 耿献国 何国亮
Format Journal Article
LanguageEnglish
Published 01.06.2014
Subjects
Conservation laws
Differential equations
Hierarchies
Integral equations
Mathematical analysis
Nonlinear evolution equations
Operators
Spectra
双Hamilton结构
层次结构
广义
微分
积分方程
线性光谱
零曲率方程
非线性发展方程
Online AccessGet full text
ISSN1674-1056
2058-3834
1741-4199
DOI10.1088/1674-1056/23/6/060201

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Summary:With the aid of the zero-curvature equation, a novel integrable hierarchy of nonlinear evolution equations associated with a 3 x 3 matrix spectral problem is proposed. By using the trace identity, the bi-Hamiltonian structures of the hierarchy are established with two skew-symmetric operators. Based on two linear spectral problems, we obtain the infinite many conservation laws of the first member in the hierarchy.
Bibliography:Zhai Yun-Yun, Geng Xian-Guo, He Guo-Liang（ School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China b） School of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, China
With the aid of the zero-curvature equation, a novel integrable hierarchy of nonlinear evolution equations associated with a 3 x 3 matrix spectral problem is proposed. By using the trace identity, the bi-Hamiltonian structures of the hierarchy are established with two skew-symmetric operators. Based on two linear spectral problems, we obtain the infinite many conservation laws of the first member in the hierarchy.
spectral problem, nonlinear evolution equations, bi-Hamiltonian structure, conservation laws
11-5639/O4
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/23/6/060201