Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bi-Hamiltonian structure as a shadow of non-Noether symmetry   In the present paper correspondence between non-Noether symmetries and
bi-Hamiltonian structures is disscussed. We show that in regular Hamiltonian
systems presence of the global bi-Hamiltonian structure is caused by symmetry
of the space of solution. As an example well known bi-Hamiltonian realisation
of Korteweg- De Vries equation is disscussed.

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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat