Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the stability of the solitary waves to the (generalized) kawahara
  equation   In this paper we investigate the orbital stability of solitary waves to the
(generalized) Kawahara equation (gKW) which is a fifth order dispersive
equation. For some values of the power of the nonlinearity, we prove the
orbital stability in the energy space H 2 (R) of two branches of even solitary
waves of gKW by combining the well-known spectral method introduced by Benjamin
[3] with continuity arguments. We construct the first family of even solitons
by applying the implicit function theorem in the neighborhood of the explicit
solitons of gKW found by Dey et al. [8]. The second family consists of even
travelling waves with low speeds. They are solutions of a constraint
minimization problem on the line and rescaling of perturbations of the soliton
of gKdV with speed 1.

22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th