Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable Couplings of Soliton Equations by Perturbations I. A General
  Theory and Application to the KdV Hierarchy   A theory for constructing integrable couplings of soliton equations is
developed by using various perturbations around solutions of perturbed soliton
equations being analytic with respect to a small perturbation parameter.
Multi-scale perturbations can be taken and thus higher dimensional integrable
couplings can be presented. The theory is applied to the KdV soliton hierarchy.
Infinitely many integrable couplings are constructed for each soliton equation
in the KdV hierarchy, which contain integrable couplings possessing quadruple
Hamiltonian formulations and two classes of hereditary recursion operators, and
integrable couplings possessing local 2+1 dimensional bi-Hamiltonian
formulations and consequent 2+1 dimensional hereditary recursion operators.

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The categories of this paper are: cs
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex