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Small Data Scattering for the One-Dimensional Nonlinear Dirac Equation with Power Nonlinearity.
- Source :
-
Communications in Partial Differential Equations . Nov2015, Vol. 40 Issue 11, p1959-2004. 46p. - Publication Year :
- 2015
-
Abstract
- We study scattering problems for the one-dimensional nonlinear Dirac equation (∂t + α∂x + iβ)Φ = λ|Φ|p−1Φ. We prove that ifp > 3 (resp.p > 3 + 1/6), then the wave operator (resp. the scattering operator) is well-defined on some 0-neighborhood of a weighted Sobolev space. In order to prove these results, we use linear operatorsD(t)xD(−t) andt∂x + x∂t − α/2, where {D(t)}t∈ℝis the free Dirac evolution group. For the reader's convenience, in an appendix we list and prove fundamental properties ofD(t)xD(−t) andt∂x + x∂t − α/2. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03605302
- Volume :
- 40
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Communications in Partial Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 110694400
- Full Text :
- https://doi.org/10.1080/03605302.2015.1081608