ANZIAM J.
44 (2002), 161-168
|
Inverse scattering for the matrix Schrödinger operator and Schrödinger operator on graphs with general self-adjoint boundary conditions
|
|
|
Abstract
|
Using 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.
|
Download the article in PDF format (size 62 Kb)
|
|
|
|