Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Cauchy problem and continuation of periodic solutions for a
  generalized Camassa-Holm equation   We consider a three-parameter family of non-linear equations with
$(p+1)-$order non-linearities. Such family includes as a particular member the
well-known $b-$equation, which encloses the famous Camassa-Holm equation. For
certain choices of the parameters we establish a global existence result and
show a scenario that prevent the wave breaking of solutions. Also, we explore
unique continuation properties for some values of the parameters.

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The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th