Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Direct and inverse scattering problems for the first-order discrete
  system associated with the derivative NLS system   The direct and inverse scattering problems are analyzed for a first-order
discrete system associated with the semi-discrete version of the derivative NLS
system. The Jost solutions, the scattering coefficients, the bound-state
dependency and norming constants are investigated and related to the
corresponding quantities for two particular discrete linear systems associated
with the semi-discrete version of the NLS system. The bound-state data set with
any multiplicities is described in an elegant manner in terms of a pair of
constant matrix triplets. Several methods are presented to the solve the
inverse problem. One of these methods involves a discrete Marchenko system
using as input the scattering data set consisting of the scattering
coefficients and the bound-state information, and this method is presented in a
way generalizable to other first-order systems both in the discrete and
continuous cases for which a Marchenko system is not yet available. Finally,
using the time-evolved scattering data set, the inverse scattering transform is
applied on the corresponding semi-discrete derivative NLS system, and in the
reflectionless case certain explicit solution formulas are presented in closed
form expressed in terms of the two matrix triplets.

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The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics