Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orbital Stability of Localized Structures via Backlund Transformations   The Backlund Transform, first developed in the context of differential
geometry, has been classically used to obtain multi-soliton states in
completely integrable infinite dimensional dynamical systems. It has recently
been used to study the stability of these special solutions. We offer here a
dynamical perspective on the Backlund Transform, prove an abstract orbital
stability theorem, and demonstrate its utility by applying it to the
sine-Gordon equation and the Toda lattice.

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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph