Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and orbital stability of standing waves for the 1D
  Schr\"odinger-Kirchhoff equation   In this paper we establish the orbital stability of standing wave solutions
associated to the one-dimensional Schr\"odinger-Kirchhoff equation. The
presence of a mixed term gives us more dispersion, and consequently, a
different scenario for the stability of solitary waves in contrast with the
corresponding nonlinear Schr\"odinger equation. For periodic waves, we exhibit
two explicit solutions and prove the orbital stability in the energy space.

29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess