Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the orbital stability of a family of traveling waves for the cubic
  Schr{\"o}dinger equation on the Heisenberg group   We consider the focusing energy-critical Schr{\"o}dinger equation on the
Heisenberg group in the radial case\[i\partial_t u-\Delta_{\mathbb{H}^1}
u=|u|^2u,\quad\Delta_{\mathbb{H}^1}=\frac{1}{4}(\partial_x^2+\partial_y^2)+(x^2+y^2)\partial_s^2,\quad(t,x,y,s)\in
\mathbb{R}\times\mathbb{H}^1,\]which is a model for non-dispersive evolution
equations. For this equation, existence of smooth global solutions and
uniqueness of weak solutions in the energy space are open problems. We are
interested in a family of ground state traveling waves parametrized by their
speed $\beta \in (-1,1)$. We show that the traveling waves of speed close to
$1$ present some orbital stability in the following sense. If the initial data
is radial and close enough to one traveling wave, then there exists a global
weak solution which stays close to the orbit of this traveling wave for all
times. A similar result is proven for the limiting system associated to this
equation.

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The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th