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On a Generalization of the Trèves Criterion for the First Integrals of the KdV Hierarchy to Higher GD Hierarchies

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Abstract

First, a new proof of the necessity of the Trèves criterion for a differential polynomialto be a first integral of the KdV hierarchy is given. This proof is much shorter than the original one and admits generalizations. Second, a similar criterion is suggested and its necessity proven for the next of the GD hierarchies which is generated by the third-order linear operator.

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References

  1. Trèves, F.: An algebraic characterization of the Korteweg-de Vries hierarchy, Duke Math. J. 108(2) (2001), 251–294.

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  2. Dickey, L. A.: Soliton Equations and Hamiltonian Systems, Adv. Ser. Math. Phys. 26, World Scientific, Singapore, 2003.

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Authors and Affiliations

  1. Department of Mathematics, Physical Sciences Center, University of Oklahoma, Norman, OK, 73019, U.S.A.

    L. A. Dickey>

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  1. L. A. Dickey>
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Dickey> , L.A. On a Generalization of the Trèves Criterion for the First Integrals of the KdV Hierarchy to Higher GD Hierarchies. Letters in Mathematical Physics 65, 187–197 (2003). https://doi.org/10.1023/B:MATH.0000010671.37908.47

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  • DOI: https://doi.org/10.1023/B:MATH.0000010671.37908.47

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