Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse scattering problems where the potential is not absolutely
  continuous on the known interior subinterval   The inverse scattering problem for the Schr$\mathrm{\ddot{o}}$dinger
operators on the line is considered when the potential is real valued and
integrable and has a finite first moment. It is shown that the potential on the
line is uniquely determined by the left (or right) reflection coefficient alone
provided that the potential is known on a finite interval and it is not
absolutely continuous on this known interval.

33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg