Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bi-Hamiltonian structures of KdV type   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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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: stat