Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-autonomous H\'{e}non-Heiles Systems   Scaling similarity solutions of three integrable PDEs, namely the
Sawada-Kotera, fifth order KdV and Kaup-Kupershmidt equations, are considered.
It is shown that the resulting ODEs may be written as non-autonomous
Hamiltonian equations, which are time-dependent generalizations of the
well-known integrable H\'{e}non-Heiles systems. The (time-dependent)
Hamiltonians are given by logarithmic derivatives of the tau-functions
(inherited from the original PDEs). The ODEs for the similarity solutions also
have inherited B\"{a}cklund transformations, which may be used to generate
sequences of rational solutions as well as other special solutions related to
the first Painlev\'{e} transcendent.

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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: math
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org