Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growth of perturbations to the peaked periodic waves in the Camassa-Holm
  equation,   Peaked periodic waves in the Camassa-Holm equation are revisited. Linearized
evolution equations are derived for perturbations to the peaked periodic waves
and linearized instability is proven both in $H^1$ and $W^{1,\infty}$ norms.
Dynamics of perturbations in $H^1$ is related to the existence of two conserved
quantities and is bounded in the full nonlinear system due to these conserved
quantities. On the other hand, perturbations to the peaked periodic wave grow
in $W^{1,\infty}$ norm and may blow up in a finite time in the nonlinear
evolution of the Camassa-Holm equation.

5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph