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Reflectionless potentials and point interactions in Pontryagin spaces

Kurasov, Pavel LU and Luger, Annemarie LU (2005) In Letters in Mathematical Physics 73(2). p.109-122
Abstract
The problem of constructing generalized point interactions of the second derivative operator in L-2( R) leading to the same scattering data as for reflectionless potentials is considered. It is proved that this problem has a solution only if extensions in Pontryagin spaces are involved. The solution of the inverse scattering problem is not unique, this is illustrated by considering the scattering data for soliton of the Korteweg-de Vries equation.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
inverse scattering, generalized Nevanlinna function, Pontryagin space
in
Letters in Mathematical Physics
volume
73
issue
2
pages
109 - 122
publisher
Springer
external identifiers
  • wos:000232985500003
  • scopus:27744461793
ISSN
0377-9017
DOI
10.1007/s11005-005-0002-1
language
English
LU publication?
yes
id
42df8a07-b557-46bd-a244-71b0ff6128dd (old id 214193)
date added to LUP
2007-08-23 16:43:08
date last changed
2017-01-01 07:25:22
@article{42df8a07-b557-46bd-a244-71b0ff6128dd,
  abstract     = {The problem of constructing generalized point interactions of the second derivative operator in L-2( R) leading to the same scattering data as for reflectionless potentials is considered. It is proved that this problem has a solution only if extensions in Pontryagin spaces are involved. The solution of the inverse scattering problem is not unique, this is illustrated by considering the scattering data for soliton of the Korteweg-de Vries equation.},
  author       = {Kurasov, Pavel and Luger, Annemarie},
  issn         = {0377-9017},
  keyword      = {inverse scattering,generalized Nevanlinna function,Pontryagin space},
  language     = {eng},
  number       = {2},
  pages        = {109--122},
  publisher    = {Springer},
  series       = {Letters in Mathematical Physics},
  title        = {Reflectionless potentials and point interactions in Pontryagin spaces},
  url          = {http://dx.doi.org/10.1007/s11005-005-0002-1},
  volume       = {73},
  year         = {2005},
}