Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic Cauchy problem for the $\mu$-Camassa-Holm equation and its
  non-quasilinear version   We solve the Cauchy problems for the $\mu$-Camassa-Holm integro-partial
differential equation of Khesin-Lenells-Misio\l{}ek and its non-quasilinear
version introduced by Qu-Fu-Liu in the complex-analytic framework. These
equations have nonlocal nature at two levels: they involve a
pseudo-differential operator of negative order and this operator is defined in
terms of an integral of the unknown function. We prove unique solvability of
the Cauchy problems and provide an estimate of the lifespan of the solutions.
Our method is the Ovsyannikov type argument by Batrostichi-Himonas-Petronilho
about a scale of Banach spaces of analytic functions, but the
non-quasilinearity is dealt with in a different way from theirs. Indeed, we use
a simple reduction which is just a nonlocal version of a classical trick.

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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph