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Wave and scattering operators for the nonlinear matrix Schrödinger equation on the half-line with a potential.
- Source :
-
Nonlinear Analysis . Feb2023, Vol. 227, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
Abstract
- We consider the nonlinear matrix Schrödinger equation on the half-line with general selfadjoint boundary condition. We prove the existence of local solutions in the corresponding energy space. Moreover, we consider the scattering problem for this problem in the scattering-supercritical regime for both generic and exceptional potentials. We construct the wave, inverse wave and scattering operators in a certain neighborhood of the origin in the scattering space Σ = H 1 ∩ L 2 , 1 for generic potentials in L 1 , 2 + η , with η > 1 / 2 , and for exceptional potentials in L 1 , 3 under further assumptions on the input data. In particular, thanks to the general boundary conditions, we are able to obtain a scattering result for the nonlinear matrix Schrödinger equation on the line with a potential and point interactions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0362546X
- Volume :
- 227
- Database :
- Academic Search Index
- Journal :
- Nonlinear Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 160586665
- Full Text :
- https://doi.org/10.1016/j.na.2022.113183