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

FAN En-gui; ZHANG Hong-qing

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Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(5): 458-464

FAN En-gui, ZHANG Hong-qing. A New Completely Integrable Liouville’s System, Its Lax Representation and Bi-Hamiltonian Structure[J]. Applied Mathematics and Mechanics, 2001, 22(5): 458-464.

Citation:

FAN En-gui, ZHANG Hong-qing. A New Completely Integrable Liouville’s System, Its Lax Representation and Bi-Hamiltonian Structure[J]. Applied Mathematics and Mechanics, 2001, 22(5): 458-464.

Citation:

FAN En-gui, ZHANG Hong-qing. A New Completely Integrable Liouville’s System, Its Lax Representation and Bi-Hamiltonian Structure[J]. Applied Mathematics and Mechanics, 2001, 22(5): 458-464.

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

FAN En-gui¹,
ZHANG Hong-qing²

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 Date: 2000-03-21
Rev Recd Date: 2001-01-05
Publish Date: 2001-05-15

Abstract

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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References(9)

References

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