Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the standing waves of the Schroedinger equation with concentrated
  nonlinearity   We study the concentrated NLS on ${\mathbf R^n}$, with power non-linearities,
driven by the fractional Laplacian, $(-\Delta)^s, s>\frac{n}{2}$. We construct
the solitary waves explicitly, in an optimal range of the parameters, so that
they belong to the natural energy space $H^s$. Next, we provide a complete
classification of their spectral stability. Finally, we show that the waves are
non-degenerate and consequently orbitally stable, whenever they are spectrally
stable.
  Incidentally, our construction shows that the soliton profiles for the
concentrated NLS are in fact exact minimizers of the Sobolev embedding
$H^s({\mathbf R^n})\hookrightarrow L^\infty({\mathbf R^n})$, which provides an
alternative calculation and justification of the sharp constants in these
inequalities.

23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga