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Bi-Hamiltonian structures of KdV type

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arxiv 1607.07020 v1 pith:CXGG7VIV submitted 2016-07-24 math-ph math.MPnlin.SI

P. Lorenzoni , A. Savoldi , R. Vitolo This is my paper · ORCID
classification math-phmath.MPnlin.SI
keywords bi-hamiltonianoperatorscompatibleexampleshamiltonianhomogeneouspairssystems
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Combining an old idea of Olver and Rosenau with the classification of second and third order homogeneous Hamiltonian operators we classify compatible trios of two-component homogeneous Hamiltonian operators. The trios yield pairs of compatible bi-Hamiltonian operators whose structure is a direct generalization of the bi-Hamiltonian pair of the KdV equation. The bi-Hamiltonian pairs give rise to multi-parametric families of bi-Hamiltonian systems. We recover known examples and we find new integrable systems whose central invariants are non-zero; this shows that new examples are not Miura-trivial.

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  1. Compatible pairs of Hamiltonian operators of the first and third orders

    nlin.SI 2026-02 conditional novelty 7.0 of 10

    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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