Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-Consistent-Field Method and $\tau$-Functional Method on Group
  Manifold in Soliton Theory: a Review and New Results   The maximally-decoupled method has been considered as a theory to apply an
basic idea of an integrability condition to certain multiple parametrized
symmetries. The method is regarded as a mathematical tool to describe a
symmetry of a collective submanifold in which a canonicity condition makes the
collective variables to be an orthogonal coordinate-system. For this aim we
adopt a concept of curvature unfamiliar in the conventional time-dependent (TD)
self-consistent field (SCF) theory. Our basic idea lies in the introduction of
a sort of Lagrange manner familiar to fluid dynamics to describe a collective
coordinate-system. This manner enables us to take a one-form which is linearly
composed of a TD SCF Hamiltonian and infinitesimal generators induced by
collective variable differentials of a canonical transformation on a group. The
integrability condition of the system read the curvature C=0. Our method is
constructed manifesting itself the structure of the group under consideration.
>...

27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat