ANZIAM J.
44 (2002), 161168

Inverse scattering for the matrix Schrödinger operator and Schrödinger operator on graphs with general selfadjoint boundary conditions


Abstract

Using a parameterisation of general selfadjoint
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.

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