Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (5): 520-527.

• 论文 • 上一篇    下一篇

A NEW COMPLETELY INTEGRABLE LIOUVILLE’S SYSTEM, ITS LAX REPRESENTATION AND BI-HAMILTONIAN STRUCTURE

范恩贵1, 张鸿庆2   

  1. 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
  • 收稿日期:2000-03-21 修回日期:2001-01-25 出版日期:2001-05-18 发布日期:2001-05-18
  • 基金资助:

    the Postdoctoral Science Foundation of China;Chinese Basic Research “Mathematical Mechanization and a Platform for Automated Reasoning”(G1998030600)

A NEW COMPLETELY INTEGRABLE LIOUVILLE’S SYSTEM, ITS LAX REPRESENTATION AND BI-HAMILTONIAN STRUCTURE

FAN En-gui1, ZHANG Hong-qing2   

  1. 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
  • Received:2000-03-21 Revised:2001-01-25 Online:2001-05-18 Published:2001-05-18
  • Supported by:

    the Postdoctoral Science Foundation of China;Chinese Basic Research “Mathematical Mechanization and a Platform for Automated Reasoning”(G1998030600)

摘要: 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.

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.

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