Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the hierarchy of partially invariant submodels of differential
  equations   It is noticed, that partially invariant solution (PIS) of differential
equations in many cases can be represented as an invariant reduction of some
PIS of the higher rank. This introduce a hierarchic structure in the set of all
PISs of a given system of differential equations. By using this structure one
can significantly decrease an amount of calculations required in enumeration of
all PISs for a given system of partially differential equations. An equivalence
of the two-step and the direct ways of construction of PISs is proved. In this
framework the complete classification of regular partially invariant solutions
of ideal MHD equations is given.

28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio