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

2009/12/10 by Erwin Suazo, Suazo, Erwin
Engineering · Mathematics · #Advanced Mathematical Physics Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Stability and Controllability of Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0912.2113

openalex publication_date 2009/12/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• The Riccati Differential Equation and a Diffusion-Type Equation
• Time decay for solutions of Schr�dinger equations with rough and time-dependent potentials

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