Abstract
AbstractWe consider the inverse scattering problem for the higher order Schrödinger operator $$H=(-\Delta )^m+q(x)$$
H
=
(
-
Δ
)
m
+
q
(
x
)
, $$m=1,2, 3,\ldots$$
m
=
1
,
2
,
3
,
…
. We show that the scattering amplitude of H at fixed angles can uniquely determines the potential q(x) under certain assumptions, which extends the early results on this problem. The uniqueness of q(x) mainly depends on the construction of the Born approximation sequence and its estimation.
Funder
the Guiding project of science and technology research plan of Hubei Provincial Department of Education
the Guiding Project of Natural Science Foundation of Hubei Province
Wuhan College Research Fund
the Hubei Provincial Enterprise-level Intelligent Application Excellent Young and Middle-aged Scientific and Technological Innovation Team
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics