Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear instability and uniqueness of the peaked periodic wave in the
  reduced Ostrovsky equation   Stability of the peaked periodic waves in the reduced Ostrovsky equation has
remained an open problem for a long time. In order to solve this problem we
obtain sharp bounds on the exponential growth of the $L^2$ norm of co-periodic
perturbations to the peaked periodic wave, from which it follows that the
peaked periodic wave is linearly unstable. We also prove that the peaked
periodic wave with parabolic profile is the unique peaked wave in the space of
periodic $L^2$ functions with zero mean and a single minimum per period.

1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys