Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Secondary Instabilities and Spatiotemporal Chaos in Parametric Surface
  Waves   A two dimensional model is introduced to study pattern formation, secondary
instabilities and the transition to spatiotemporal chaos (weak turbulence) in
parametric surface waves. The stability of a periodic standing wave state above
onset is studied against Eckhaus, zig-zag and transverse amplitude modulations
(TAM) as a function of the control parameter $\varepsilon$ and the detuning. A
mechanism leading to a finite threshold for the TAM instability is identified.
Numerical solutions of the model are in agreement with the stability diagram,
and also reveal the existence of a transition to spatiotemporal chaotic states
at a finite $\varepsilon$. Power spectra of temporal fluctuations in the
chaotic state are broadband, decaying as a power law of the frequency
$\omega^{-z}$ with $z \approx 4.0$.

18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio