Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instabilities of Higher-Order Parametric Solitons. Filamentation versus
  Coalescence   We investigate stability and dynamics of higher-order solitary waves in
quadratic media, which have a central peak and one or more surrounding rings.
We show existence of two qualitatively different behaviours. For positive phase
mismatch the rings break up into filaments which move radially to initial ring.
For sufficient negative mismatches rings are found to coalesce with central
peak, forming a single oscillating filament.

15
The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
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The categories of this paper are: eess