Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrability and Vesture for Harmonic Maps into Symmetric Spaces   After giving the most general formulation to date of the notion of
integrability for axially symmetric harmonic maps from R^3 into symmetric
spaces, we give a complete and rigorous proof that, subject to some mild
restrictions on the target, all such maps are integrable. Furthermore, we prove
that a variant of the inverse scattering method, called vesture (dressing) can
always be used to generate new solutions for the harmonic map equations
starting from any given solution. In particular we show that the problem of
finding N-solitonic harmonic maps into a noncompact Grassmann manifold
SU(p,q)/S(U(p) x U(q)) is completely reducible via the vesture (dressing)
method to a problem in linear algebra which we prove is solvable in general. We
illustrate this method by explicitly computing a 1-solitonic harmonic map for
the two cases (p = 1, q = 1) and (p = 2, q = 1); and we show that the family of
solutions obtained in each case contains respectively the Kerr family of
solutions to the Einstein vacuum equations, and the Kerr-Newman family of
solutions to the Einstein-Maxwell equations.

27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th