Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable embedded solitons   Stable embedded solitons are discovered in the generalized third-order
nonlinear Schroedinger equation. When this equation can be reduced to a
perturbed complex modified KdV equation, we developed a soliton perturbation
theory which shows that a continuous family of sech-shaped embedded solitons
exist and are nonlinearly stable. These analytical results are confirmed by our
numerical simulations. These results establish that, contrary to previous
beliefs, embedded solitons can be robust despite being in resonance with the
linear spectrum.

1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn