Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-time momentum and actions behaviour of energy-preserving methods
  for semilinear wave equations via spatial spectral semi-discretizations   As is known that wave equations have physically very important properties
which should be respected by numerical schemes in order to predict correctly
the solution over a long time period. In this paper, the long-time behaviour of
momentum and actions for energy-preserving methods is analysed for semilinear
wave equations. A full discretisation of wave equations is derived and analysed
by firstly using a spectral semi-discretisation in space and then by applying
the adopted average vector field (AAVF) method in time. This numerical scheme
can exactly preserve the energy of the semi-discrete system. The main theme of
this paper is to analyse another important physical property of the scheme. It
is shown that this scheme yields near conservation of a modified momentum and
modified actions over long times. Both the results are rigorously proved based
on the technique of modulated Fourier expansions in two stages. First a
multi-frequency modulated Fourier expansion of the AAVF method is constructed
and then two almost-invariants of the modulation system are derived.

27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat