Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A direct algorithm of one-dimensional optimal system for the group
  invariant solutions   A direct and systematic algorithm is proposed to find one-dimensional optimal
system for the group invariant solutions, which is attributed to the
classification of its corresponding one-dimensional Lie algebra. Since the
method is based on different values of all the invariants, the process itself
can both guarantee the comprehensiveness and demonstrate the inequivalence of
the optimal system, with no further proof. To illustrate our method more
clearly , we give a couple of well-known examples: the Korteweg-de Vries (KdV)
equation and the heat equation.

23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
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
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn