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A New Completely Integrable Liouville's System, its Lax Representation and Bi-Hamiltonian Structure

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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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Authors and Affiliations

  1. Institute of Mathematics, Fudan University, Shanghai, 200433, P R China

    En-gui Fan

  2. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, P R China

    Hong-qing Zhang

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  1. En-gui Fan
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  2. Hong-qing Zhang
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Fan, Eg., Zhang, Hq. A New Completely Integrable Liouville's System, its Lax Representation and Bi-Hamiltonian Structure. Applied Mathematics and Mechanics 22, 520–527 (2001). https://doi.org/10.1023/A:1016355230164

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  • DOI: https://doi.org/10.1023/A:1016355230164

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