Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A class of stable perturbations for a minimal mass soliton in three
  dimensional saturated nonlinear Schr\"odinger equations   In this result, we develop the techniques of \cite{KS1} and \cite{BW} in
order to determine a class of stable perturbations for a minimal mass soliton
solution of a saturated, focusing nonlinear Schr\"odinger equation {c} i u_t +
\Delta u + \beta (|u|^2) u = 0 u(0,x) = u_0 (x), in $\reals^3$. By projecting
into a subspace of the continuous spectrum of $\mathcal{H}$ as in \cite{S1},
\cite{KS1}, we are able to use a contraction mapping similar to that from
\cite{BW} in order to show that there exist solutions of the form e^{i
\lambda_{\min} t} (R_{min} + e^{i \mathcal{H} t} \phi + w(x,t)), where $e^{i
\mathcal{H} t} \phi + w(x,t)$ disperses as $t \to \infty$. Hence, we have long
time persistance of a soliton of minimal mass despite the fact that these
solutions are shown to be nonlinearly unstable in \cite{CP1}.

9
The categories of this paper are: nlin
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat