Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear instability of stationary solutions for the Korteweg-de Vries
  equation on a star graph   The aim of this work is to establish a linear instability criterium of
stationary solutions for the Korteweg-de Vries model on a star graph with a
structure represented by a finite collections of semi-infinite edges. By
considering a boundary condition of $\delta$-type interaction at the
graph-vertex, we show that the continuous tail and bump profiles are linearly
unstable in a balanced star graph. The use of the analytic perturbation theory
of operators and the extension theory of symmetric operators is a piece
fundamental in our stability analysis.
  The arguments presented in this investigation has prospects for the study of
the instability of stationary waves solutions of other nonlinear evolution
equations on star graphs.

13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph