Reflectionless potentials and point interactions in Pontryagin spaces
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/214193
- author
- Kurasov, Pavel LU and Luger, Annemarie LU
- organization
- publishing date
- 2005
- 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
- 2016-04-01 17:08:27
- date last changed
- 2022-01-29 00:39:13
@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}}, keywords = {{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}}, doi = {{10.1007/s11005-005-0002-1}}, volume = {{73}}, year = {{2005}}, }