一个新的Liouville可积系统及其Lax表示, Bi-Hamilton结构

基金项目: 中国博士后基金资助课题;国家基础研究重大课题“数学机械化及自动推理平台”资助课题(G1998030600)

A New Completely Integrable Liouville’s System, Its Lax Representation and Bi-Hamiltonian Structure

1.
Institute of Mathematics, Fudan University, Shanghai 200433, P R China;
2.
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P R China

摘要: 从一个特征值问题出发,首先推导一族非线性发展方程,其中包括著名MKdV方程做为特殊约化,进一步证明这族方程在Liounille意义下可积并具有Bi-Hamilton结构。而在位势函数和特征函数之间的一定约束下,特征值问题被非线性化为一完全可积的有限维Hamilton系统。
- 可积系统 /
- Lax表示 /
- Bi-Hamilton结构
Abstract: A new isospectral problem and the corresponding hierarchy of nonlinear evolution equations is presented.As a reduction,the well-known MKdV equation is obtained.It is shown that the hierarchy of equations is integrable in Liouville's sense and possesses Bi-Hamiltonian structure.Under the constraint between the potentials and eigenfunctions,the eigenvalue problem can be nonlinearized as a finite dimensional completely integrable system.
- integrable system /
- Lax representation /
- Bi-Hamiltonian structure

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