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A New Hierarchy of Lax and Liouville Integrable Evolution Equations Associated with an Isospectral Problem in the Loop Algebra Ã2

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Abstract

In this paper, an isospectral problem with five potentials is investigated in loop algebra à 2 such that a new hierarchy of evolution equations with five arbitrary functions is obtained. And then by fixing the five arbitrary functions to be certain functions and using the trace identity, the generalized Hamiltonian structure of the hierarchy of evolution equations is given. It is shown that this hierarchy of equations is Liouville integrable. Finally some special cases of the isospectral problem are also given.

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Authors and Affiliations

  1. Key Laboratory of Mathematics Mechanization, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Zhenya Yan

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  1. Zhenya Yan
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Correspondence to Zhenya Yan.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 10401039) and the National Key Basic Research Project of China (No. 2004CB318000).

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Yan, Z. A New Hierarchy of Lax and Liouville Integrable Evolution Equations Associated with an Isospectral Problem in the Loop Algebra Ã2 . Jrl Syst Sci & Complex 19, 301–306 (2006). https://doi.org/10.1007/s11424-006-0301-3

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  • DOI: https://doi.org/10.1007/s11424-006-0301-3

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