L^p-L^p' Estimates for the Nonlinear Schroedinger Equation on the Line and Inverse Scattering for the Nonlinear Schroedinger Equation with a Potential
Weder, Ricardo
arXiv, 9806008 / Harvested from arXiv
Text on arXiv
In this paper I prove a L^p-L^p' estimate for the solutions of the one-dimensional Schroedinger equation with a potential in L^1_gamma where in the generic case gamma > 3/2 and in the exceptional case (i.e. when there is a half-bound state of zero energy) gamma > 5/2. I use this estimate to construct the scattering operator for the nonlinear Schroedinger equation with a potential. I prove moreover, that the low-energy limit of the scattering operator uniquely determines the potential and the nonlinearity using a method that allows as well for the reconstruction of the potential and of the nonlinearity.
Publié le : 1998-06-12
Classification:  Mathematical Physics,  Mathematics - Analysis of PDEs,  35P, 81U (Primary) 35Q, 35R,34B (Secondary) 
@article{9806008,
     author = {Weder, Ricardo},
     title = {L^p-L^p' Estimates for the Nonlinear Schroedinger Equation on the Line
  and Inverse Scattering for the Nonlinear Schroedinger Equation with a
  Potential},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9806008}
}

Weder, Ricardo. L^p-L^p' Estimates for the Nonlinear Schroedinger Equation on the Line
  and Inverse Scattering for the Nonlinear Schroedinger Equation with a
  Potential. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9806008/