On Schroedinger Equation with Time-Dependent Quadratic Hamiltonian in $R^d$
Mathematical Physics
2010-04-12 v3 math.MP
Abstract
We study solutions to the Cauchy problem for the linear and nonlinear Schroedinger equation with a quadratic Hamiltonian depending on time. For the linear case the evolution operator can be expressed as an integral operator with the explicit formula for the kernel. As a consequence, conditions for local and global in time Strichartz estimates can be established. For the nonlinear case we show local well-posedness. As a particular case we obtain well-posedness for the damped harmonic nonlinear Schroedinger equation.
Keywords
Cite
@article{arxiv.0912.2113,
title = {On Schroedinger Equation with Time-Dependent Quadratic Hamiltonian in $R^d$},
author = {Erwin Suazo},
journal= {arXiv preprint arXiv:0912.2113},
year = {2010}
}
Comments
16 pages