Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A KAM Theorem for Two-dimensional Nonlinear Schr\"odinger Equations   We prove an infinite dimensional KAM theorem. As an application, we use the
theorem to study the two-dimensional nonlinear Schr\"{o}dinger equation
$$iu_t-\triangle u +|u|^2u+\frac{\partial{f(x,u,\bar u)}}{\partial{\bar u}}=0,
\quad t\in\Bbb R, x\in\Bbb T^2$$ with periodic boundary conditions, where the
nonlinearity $\displaystyle f(x,u,\bar u)=\sum_{j,l,j+l\geq6}a_{jl}(x)u^j\bar
u^l$, $a_{jl}=a_{lj}$ is a real analytic function in a neighborhood of the
origin. We obtain for the equation a Whitney smooth family of small--amplitude
quasi--periodic solutions which are partially hyperbolic.

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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: q-bio