Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On nonparaxial nonlinear Schr\"odinger-type equations   In this paper the one-dimensional nonparaxial nonlinear Schr\"odinger
equation is considered. This was proposed as an alternative to the classical
nonlinear Schr\"odinger equation in those situations where the assumption of
paraxiality may fail. The paper contributes to the mathematical properties of
the equation in a two-fold way. First, some theoretical results on linear
well-posedness, Hamiltonian and multi-symplectic formulations are derived. Then
we propose to take into account these properties in order to deal with the
numerical approximation. In this sense, different numerical procedures that
preserve the Hamiltonian and multi-symplectic structures are discussed and
illustrated with numerical experiments.

37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio