Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic stability in the energy space for dark solitons of the
  Landau-Lifshitz equation   We prove the asymptotic stability in the energy space of non-zero speed
solitons for the one-dimensional Landau-Lifshitz equation with an easy-plane
anisotropy. More precisely, we show that any solution corresponding to an
initial datum close to a soliton with non-zero speed, is weakly convergent in
the energy space as time goes to infinity, to a soliton with a possible
different non-zero speed, up to the invariances of the equation. Our analysis
relies on the ideas developed by Martel and Merle for the generalized
Korteweg-de Vries equations. We use the Madelung transform to study the problem
in the hydrodynamical framework. In this framework, we rely on the orbital
stability of the solitons and the weak continuity of the flow in order to
construct a limit profile. We next derive a monotonicity formula for the
momentum, which gives the localization of the limit profile. Its smoothness and
exponential decay then follow from a smoothing result for the localized
solutions of the Schr\"odinger equations. Finally, we prove a Liouville type
theorem, which shows that only the solitons enjoy these properties in their
neighbourhoods.

26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas