Inverse scattering on the half-line for energy-dependent Schrödinger equations

Hryniv, Rostyslav; Manko, Stepan

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dc.contributor.author	Hryniv, Rostyslav
dc.contributor.author	Manko, Stepan
dc.date.accessioned	2021-06-30T12:03:57Z
dc.date.available	2021-06-30T12:03:57Z
dc.date.issued	2020-08-31
dc.identifier.citation	Hryniv R.O. and Manko S. S. Inverse scattering on the half-line for energy-dependent Schrödinger equations // Inverse Problems. 2020. V. 36, paper id 095002 (15pp), https://doi.org/10.1088/1361-6420/aba416	uk
dc.identifier.uri	https://er.ucu.edu.ua/handle/1/2713
dc.description.abstract	In this paper, we study the inverse scattering problem for energy-dependent Schrödinger equations on the half-line with energy-dependent boundary conditions at the origin. Under certain positivity and very mild regularity assumptions, we transform this scattering problem to the one for non-canonical Dirac systems and show that, in turn, the latter can be placed within the known scattering theory for ZS-AKNS systems. This allows us to give a complete description of the corresponding scattering functions S for the class of problems under consideration and justify an algorithm of reconstructing the problem from S.	uk
dc.language.iso	en	uk
dc.publisher	IOP Publishing	uk
dc.rights	Attribution-NonCommercial-ShareAlike 3.0 United States	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-sa/3.0/us/	*
dc.subject
dc.subject	Schrödinger equation
dc.subject	inverse scattering
dc.subject	energy-dependent potentials
dc.title	Inverse scattering on the half-line for energy-dependent Schrödinger equations	uk
dc.type	Article	uk
dc.status	Опублікований і розповсюджений раніше	uk
dc.identifier.doi	https://doi.org/10.1088/1361-6420/aba416
dc.description.abstracten	In this paper, we study the inverse scattering problem for energy-dependent Schrödinger equations on the half-line with energy-dependent boundary conditions at the origin. Under certain positivity and very mild regularity assumptions, we transform this scattering problem to the one for non-canonical Dirac systems and show that, in turn, the latter can be placed within the known scattering theory for ZS-AKNS systems. This allows us to give a complete description of the corresponding scattering functions S for the class of problems under consideration and justify an algorithm of reconstructing the problem from S.	uk
dc.relation.source	Inverse Problems	uk