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

Zhenya Yan

Journal of Systems Science & Complexity ›› 2006, Vol. 19 ›› Issue (3) : 301-306.

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Journal of Systems Science & Complexity ›› 2006, Vol. 19 ›› Issue (3) : 301-306.
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A New Hierarchy of Lax and Liouville Integrable Evolution Equations Associated with an Isospectral Problem in the Loop Algebra Ã2

  • Zhenya Yan
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Abstract

In this paper, an isospectral problem with five potentials is investigated in loop algebra A~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.

Key words

Isospectral problem / loop algebra / Lax integrable / Liouville integrable / Hamiltonian structure

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Zhenya Yan. A New Hierarchy of Lax and Liouville Integrable Evolution Equations Associated with an Isospectral Problem in the Loop Algebra Ã2 . Journal of Systems Science and Complexity, 2006, 19(3): 301-306
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