Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lie symmetries and singularity analysis for generalized shallow-water
  equations   We perform a complete study by using the theory of invariant point
transformations and the singularity analysis for the generalized Camassa-Holm
equation and the generalized Benjamin-Bono-Mahoney equation. From the Lie
theory we find that the two equations are invariant under the same
three-dimensional Lie algebra which is the same Lie algebra admitted by the
Camassa-Holm equation. We determine the one-dimensional optimal system for the
admitted Lie symmetries and we perform a complete classification of the
similarity solutions for the two equations of our study. The reduced equations
are studied by using the point symmetries or the singularity analysis. Finally,
the singularity analysis is directly applied on the partial differential
equations from where we infer that the generalized equations of our study pass
the singularity test and are integrable.

34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org