Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A self-adaptive moving mesh method for the short pulse equation via its
  hodograph link to the sine-Gordon equation   The short pulse equation was introduced by Schaefer--Wayne (2004) for
modeling the propagation of ultrashort optical pulses. While it can describe a
wide range of solutions, its ultrashort pulse solutions with a few cycles,
which the conventional nonlinear Schroedinger equation does not possess, have
drawn much attention. In such a region, existing numerical methods turn out to
require very fine numerical mesh, and accordingly are computationally
expensive. In this paper, we establish a new efficient numerical method by
combining the idea of the hodograph transformation and the structure-preserving
numerical methods. The resulting scheme is a self-adaptive moving mesh scheme
that can successfully capture not only the ultrashort pulses but also exotic
solutions such as loop soliton solutions.

22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex