Inverse scattering for the matrix Schrödinger operator and Schrödinger operator on graphs with general self-adjoint boundary conditions
Keyword(s):
AbstractUsing a parameterisation of general self-adjoint boundary conditions in terms of Lagrange planes we propose a scheme for factorising the matrix Schrödinger operator and hence construct a Darboux transformation, an interesting feature of which is that the matrix potential and boundary conditions are altered under the transformation. We present a solution of the inverse problem in the case of general boundary conditions using a Marchenko equation and discuss the specialisation to the case of a graph with trivial compact part, that is, with diagonal matrix potential.
Trace formulas for the matrix Schrödinger operator on the half-line with general boundary conditions
2016 ◽
Vol 57
(11)
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pp. 112101
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2017 ◽
Vol 58
(10)
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pp. 102107
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Keyword(s):
2020 ◽
Vol 69
(1)
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pp. 486-510
2019 ◽
Vol 27
(2)
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pp. 217-223
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Keyword(s):
2012 ◽
Vol 350
(19-20)
◽
pp. 891-896
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