Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recovery of zeroth order coefficients in non-linear wave equations   This paper is concerned with the resolution of an inverse problem related to
the recovery of a scalar (potential) function $V$ from the source to solution
map, of the semi-linear equation $(\Box_{g}+V)u+u^3=0$ on a globally hyperbolic
Lorentzian manifold $(M,g)$. We first study the simpler model problem where the
geometry is the Minkowski space and prove the uniqueness of $V$ through the use
of geometric optics and a three-fold wave interaction arising from the cubic
non-linearity. Subsequently, the result is generalized to globally hyperbolic
Lorentzian manifolds by using Gaussian beams.

16
The categories of this paper are: stat
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph