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Inverse scattering for the matrix Schrödinger operator and Schrödinger operator on graphs with general self-adjoint boundary conditions

Published online by Cambridge University Press:  17 February 2009

M. S. Harmer
M. S. Harmer
Affiliation:
Department of Mathematics, University of Auckland, New Zealand; e-mail: [email protected].
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 1 , July 2002 , pp. 161 - 168
Copyright
Copyright © Australian Mathematical Society 2002

References

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