Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the continuum limit for discrete NLS with long-range lattice
  interactions   We consider a general class of discrete nonlinear Schroedinger equations
(DNLS) on the lattice $h \mathbb{Z}$ with mesh size $h>0$. In the continuum
limit when $h \to 0$, we prove that the limiting dynamics are given by a
nonlinear Schroedinger equation (NLS) on $\mathbb{R}$ with the fractional
Laplacian $(-\Delta)^\alpha$ as dispersive symbol. In particular, we obtain
that fractional powers $1/2 < \alpha < 1$ arise from long-range lattice
interactions when passing to the continuum limit, whereas NLS with the
non-fractional Laplacian $-\Delta$ describes the dispersion in the continuum
limit for short-range lattice interactions (e.g., nearest-neighbor
interactions).
  Our results rigorously justify certain NLS model equations with fractional
Laplacians proposed in the physics literature. Moreover, the arguments given in
our paper can be also applied to discuss the continuum limit for other lattice
systems with long-range interactions.

35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an