Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a Lagrangian reduction and a deformation of completely integrable
  systems   We develop a theory of Lagrangian reduction on loop groups for completely
integrable systems after having exchanged the role of the space and time
variables in the multi-time interpretation of integrable hierarchies. We then
insert the Sobolev norm $H^1$ in the Lagrangian and derive a deformation of the
corresponding hierarchies. The integrability of the deformed equations is
altered and a notion of weak integrability is introduced. We implement this
scheme in the AKNS and SO(3) hierarchies and obtain known and new equations.
Among them we found two important equations, the Camassa-Holm equation, viewed
as a deformation of the KdV equation, and a deformation of the NLS equation.

1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas