Projective-geometric aspects of homogeneous third-order Hamiltonian operators

Eugene V. Ferapontov; Maxim V. Pavlov; Raffaele F. Vitolo

Projective-geometric aspects of homogeneous third-order Hamiltonian operators

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arxiv 1401.7235 v1 pith:ZQ5MU7EA submitted 2014-01-28 nlin.SI

Eugene V. Ferapontov , Maxim V. Pavlov , Raffaele F. Vitolo This is my paper · ORCID

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keywords operatorshamiltonianhomogeneousthird-orderaspectscompletecomplexescomponents

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We investigate homogeneous third-order Hamiltonian operators of differential-geometric type. Based on the correspondence with quadratic line complexes, a complete list of such operators for two and three components is obtained.

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Compatible pairs of Hamiltonian operators of the first and third orders
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Compatibility of a first-order weakly nonlocal Hamiltonian operator with a third-order Hamiltonian operator is equivalent to algebraic equations, with the first-order metric fixed by a structure formula in terms of Ha...

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