Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse scattering at fixed energy on three-dimensional asymptotically
  hyperbolic St{\"a}ckel manifolds   In this paper, we study an inverse scattering problem at fixed energy on
three-dimensional asymptotically hyperbolic St{\"a}ckel manifolds having the
topology of toric cylinders and satisfying the Robertson condition. On these
manifolds the Helmholtz equation can be separated into a system of a radial ODE
and two angular ODEs. We can thus decompose the full scattering operator onto
generalized harmonics and the resulting partial scattering matrices consist in
a countable set of $2 \times 2$ matrices whose coefficients are the so-called
transmission and reflection coefficients. It is shown that the reflection
coefficients are nothing but generalized Weyl-Titchmarsh functions associated
with the radial ODE. Using a novel multivariable version of the Complex Angular
Momentum method, we show that the knowledge of the scattering operator at a
fixed non-zero energy is enough to determine uniquely the metric of the
three-dimensional St{\"a}ckel manifold up to natural obstructions.

22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics