Reflectionless potentials and point interactions in Pontryagin spaces

Pavel Kurasov; Annemarie Luger

doi:10.1007/s11005-005-0002-1

Reflectionless potentials and point interactions in Pontryagin spaces

Pavel Kurasov, Annemarie Luger

Mathematics (Faculty of Engineering)

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	109-122
Journal	Letters in Mathematical Physics
Volume	73
Issue number	2
DOIs	https://doi.org/10.1007/s11005-005-0002-1
Publication status	Published - 2005

Subject classification (UKÄ)

Mathematical Sciences

Free keywords

inverse scattering
generalized Nevanlinna function
Pontryagin space

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10.1007/s11005-005-0002-1

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title = "Reflectionless potentials and point interactions in Pontryagin spaces",

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.",

keywords = "inverse scattering, generalized Nevanlinna function, Pontryagin space",

author = "Pavel Kurasov and Annemarie Luger",

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AU - Kurasov, Pavel

AU - Luger, Annemarie

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - inverse scattering

KW - generalized Nevanlinna function

KW - Pontryagin space

U2 - 10.1007/s11005-005-0002-1

DO - 10.1007/s11005-005-0002-1

M3 - Article

SN - 0377-9017

VL - 73

SP - 109

EP - 122

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 2

ER -

Reflectionless potentials and point interactions in Pontryagin spaces

Abstract

Subject classification (UKÄ)

Free keywords

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Cite this