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arXiv · 0912.2113

On Schroedinger Equation with Time-Dependent Quadratic Hamiltonian in $R^d$

Erwin Suazo
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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.

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Erwin Suazo. 2010-04-09. On Schroedinger Equation with Time-Dependent Quadratic Hamiltonian in $R^d$. https://arxiv.org/abs/0912.2113

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