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Direct and inverse scattering problems for the firstā€order discrete system associated with the derivative NLS system

Authors :
Tuncay Aktosun
R. Ercan
Source :
Studies in Applied Mathematics. 148:270-339
Publication Year :
2021
Publisher :
Wiley, 2021.

Abstract

The direct and inverse scattering problems are analyzed for a first-order discrete system associated with the semi-discrete version of the derivative NLS system. The Jost solutions, the scattering coefficients, the bound-state dependency and norming constants are investigated and related to the corresponding quantities for two particular discrete linear systems associated with the semi-discrete version of the NLS system. The bound-state data set with any multiplicities is described in an elegant manner in terms of a pair of constant matrix triplets. Several methods are presented to the solve the inverse problem. One of these methods involves a discrete Marchenko system using as input the scattering data set consisting of the scattering coefficients and the bound-state information, and this method is presented in a way generalizable to other first-order systems both in the discrete and continuous cases for which a Marchenko system is not yet available. Finally, using the time-evolved scattering data set, the inverse scattering transform is applied on the corresponding semi-discrete derivative NLS system, and in the reflectionless case certain explicit solution formulas are presented in closed form expressed in terms of the two matrix triplets.<br />71 pages

Details

ISSN :
14679590 and 00222526
Volume :
148
Database :
OpenAIRE
Journal :
Studies in Applied Mathematics
Accession number :
edsair.doi.dedup.....a3c2bfd386ea01182bdc9e59c13f885e
Full Text :
https://doi.org/10.1111/sapm.12441