Inverse scattering problem for Sturm–Liouville operators with Bessel singularities on noncompact star-type graphs

2015 ◽  
Vol 31 (12) ◽  
pp. 125006 ◽  
Author(s):  
Mikhail Ignatyev
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Sturm Liouville ◽  
Liouville Operators

scholarly journals Inverse scattering problem for Sturm-Liouville operator on one-vertex noncompact graph with a cycle

2011 ◽  
Vol 42 (3) ◽  
pp. 365-384 ◽  
Author(s):  
Mikhail Ignatiev
Keyword(s):  
Inverse Problem ◽  
Differential Operator ◽  
Uniqueness Theorem ◽  
Inverse Scattering ◽  
Liouville Operator ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Order Differential Operator ◽  
Sturm Liouville ◽  
Noncompact Graph

A scattering problem is studied for second-order differential operator on one-vertex noncompact graph with a cycle and with standard matching conditions in the vertex. A uniqueness theorem for a corresponding inverse problem is proved and a procedure for solving the problem is provided.

scholarly journals Inverse scattering problem for Sturm-Liouville operator on non-compact A-graph. Uniqueness result.

2015 ◽  
Vol 46 (4) ◽  
pp. 401-422 ◽  
Author(s):  
Mikhail Ignatyev
Keyword(s):  
Inverse Problem ◽  
Differential Operators ◽  
Scattering Problem ◽  
Spectral Characteristics ◽  
Inverse Scattering Problem ◽  
Uniqueness Result ◽  
Scattering Data ◽  
Scattering Problems ◽  
Sturm Liouville ◽  
Liouville Operators

We consider a connected metric graph with the following property: each two cycles can have at most one common point. Such graphs are called A-graphs. On noncompact A-graph we consider a scattering problem for Sturm--Liouville differential operator with standard matching conditions in the internal vertices. Transport, spectral and scattering problems for differential operators on graphs appear frequently in mathematics, natural sciences and engineering. In particular, direct and inverse problems for such operators are used to construct and study models in mechanics, nano-electronics, quantum computing and waveguides. The most complete results on (both direct and inverse) spectral problems were achieved in the case of Sturm--Liouville operators on compact graphs, in the noncompact case there are no similar general results. In this paper, we establish some properties of the spectral characteristics and investigate the inverse problem of recovering the operator from the scattering data. A uniqueness theorem for such inverse problem is proved.

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