Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering for 1D cubic NLS and singular vortex dynamics   In this paper we study the stability of the self-similar solutions of the
binormal flow, which is a model for the dynamics of vortex filaments in fluids
and super-fluids. These particular solutions $\chi_a(t,x)$ form a family of
evolving regular curves of $\mathbb R^3$ that develop a singularity in finite
time, indexed by a parameter $a>0$. We consider curves that are small regular
perturbations of $\chi_a(t_0,x)$ for a fixed time $t_0$. In particular, their
curvature is not vanishing at infinity, so we are not in the context of known
results of local existence for the binormal flow. Nevertheless, we construct in
this article solutions of the binormal flow with these initial data. Moreover,
these solutions become also singular in finite time. Our approach uses the
Hasimoto transform what leads us to study the long-time behavior of a 1D cubic
NLS equation with time-depending coefficients and small regular perturbations
of the constant solution as initial data. We prove asymptotic completeness for
this equation in appropriate function spaces.

26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess