Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The general differential-geometric structure of multidimensional
  Delsarte transmutation operators in parametric functional spaces and their
  applications in soliton theory. Part 2   The structure properties of multidimensional Delsarte transmutation operators
in parametirc functional spaces are studied by means of differential-geometric
tools. It is shown that kernels of the corresponding integral operator
expressions depend on the topological structure of related homological cycles
in the coordinate space. As a natural realization of the construction presented
we build pairs of Lax type commutive differential operator expressions related
via a Darboux-Backlund transformation having a lot of applications in solition
theory. Some results are also sketched concerning theory of Delsarte
transmutation operators for affine polynomial pencils of multidimensional
differential operators.

21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc