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Direct and inverse scattering problems for the firstāorder discrete system associated with the derivative NLS system
- 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
- Subjects :
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
Inverse scattering transform
Scattering
Applied Mathematics
Mathematical analysis
Linear system
FOS: Physical sciences
Mathematical Physics (math-ph)
Inverse problem
37K10 37K15 81U40
Discrete system
Matrix (mathematics)
Inverse scattering problem
Exactly Solvable and Integrable Systems (nlin.SI)
Constant (mathematics)
Mathematical Physics
Mathematics
Subjects
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