Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cross-Newell equations for hexagons and triangles   The Cross-Newell equations for hexagons and triangles are derived for general
real gradient systems, and are found to be in flux-divergence form. Specific
examples of complex governing equations that give rise to hexagons and
triangles and which have Lyapunov functionals are also considered, and explicit
forms of the Cross-Newell equations are found in these cases. The general
nongradient case is also discussed; in contrast with the gradient case, the
equations are not flux-divergent. In all cases, the phase stability boundaries
and modes of instability for general distorted hexagons and triangles can be
recovered from the Cross-Newell equations.

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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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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: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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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: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: physics