The inverse scattering problem for Schrödinger and Klein–Gordon equations with a nonlocal nonlinearity
✍ Scribed by Hironobu Sasaki
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 206 KB
- Volume
- 66
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
dedicated to professors jean ginibre and walter a. strauss on their sixtieth birthdays We show that when n=1 and 2, the scattering operators are well-defined in the whole energy space for nonlinear Klein Gordon and Schro dinger equations in R 1+n with nonlinearity |u| p&1 u, p>1+4Ân. Such results h
In this paper I prove a L p &L p estimate for the solutions to the one-dimensional Schro dinger equation with a potential in L 1 # where in the generic case #>3Â2 and in the exceptional case (i.e., when there is a half-bound state of zero energy) #>5Â2. I use this estimate to construct the scatterin