Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of smooth solitary waves in the b-Camassa-Holm equation   We derive the precise stability criterion for smooth solitary waves in the
b-family of Camassa-Holm equations. The smooth solitary waves exist on the
constant background. In the integrable cases b = 2 and b = 3, we show
analytically that the stability criterion is satisfied and smooth solitary
waves are orbitally stable with respect to perturbations in $H^3(\mathbb{R})$.
In the non-integrable cases, we show numerically and asymptotically that the
stability criterion is satisfied for every b > 1. The orbital stability theory
relies on a different Hamiltonian formulation compared to the Hamiltonian
formulations available in the integrable cases.

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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph