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Well-posedness of the mixed-fractional nonlinear Schrödinger equation on R2
- Source :
- Partial Differential Equations in Applied Mathematics, Vol 6, Iss , Pp 100406- (2022)
- Publication Year :
- 2022
- Publisher :
- Elsevier, 2022.
-
Abstract
- We investigate the well-posedness theory of the 2-D fractional nonlinear Schrödinger equation (NLSE) with a mixed degree of derivatives. Motivated by models in optics and photonics where the light propagation is governed by non-quadratic, fractional, and anisotropic dispersion profile, this paper presents first results in this direction. Dispersive estimates are developed in the context of anisotropic Sobolev spaces defined by inhomogeneous symbols. The main model is shown to exhibit scattering for small data in the scaling-critical space. Furthermore the continuity of solution with respect to the dispersion parameter is shown on a compact time interval.
Details
- Language :
- English
- ISSN :
- 26668181
- Volume :
- 6
- Issue :
- 100406-
- Database :
- Directory of Open Access Journals
- Journal :
- Partial Differential Equations in Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.64a48e55ac2742b88fa10c38b335b3a4
- Document Type :
- article
- Full Text :
- https://doi.org/10.1016/j.padiff.2022.100406