Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonian Flows of Curves in symmetric spaces G/SO(N) and Vector
  Soliton Equations of mKdV and Sine-Gordon Type   The bi-Hamiltonian structure of the two known vector generalizations of the
mKdV hierarchy of soliton equations is derived in a geometrical fashion from
flows of non-stretching curves in Riemannian symmetric spaces G/SO(N). These
spaces are exhausted by the Lie groups G=SO(N+1),SU(N). The derivation of the
bi-Hamiltonian structure uses a parallel frame and connection along the curves,
tied to a zero curvature Maurer-Cartan form on G, and this yields the vector
mKdV recursion operators in a geometric O(N-1)-invariant form. The kernel of
these recursion operators is shown to yield two hyperbolic vector
generalizations of the sine-Gordon equation. The corresponding geometric curve
flows in the hierarchies are described in an explicit form, given by wave map
equations and mKdV analogs of Schrodinger map equations.

17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci