Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A KAM theorem with applications to partial equations of higher dimension   The existence of lower dimensional KAM tori is shown for a class of nearly
integrable Hamiltonian systems where the second Melnikov's conditions are
eliminated. As a consequence, it is proved that there exist many invariant tori
and thus quasi-periodic solutions for nonlinear wave equations, Schr\"odinger
equations and other equations of higher spatial dimension.

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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-alg