Time Dependent Phase Space Filters

This book introduces an interesting and alternative way to design absorbing boundary conditions (ABCs) for quantum wave equations, basically the nonlinear Schrödinger equation. The focus of this book is the application of the phase space filter approach to derive accurate radiation conditions for Schrödinger equations.

Researchers who are interested in partial differential equations and mathematical physics might find this book appealing.

Discusses about frames and their application in details Provides alternative approach to absorbing boundary conditions Presents derivation of accurate radiation conditions for Schrödinger equations

Autorentext

Avy Soffer is a professor at the Department of Mathematics, Rutgers University. He obtained his PhD at Tel-Aviv University in Mathematical-Physics in 1984. He was a Sloan fellow in 1988, ICM invited speaker in 2006, and AMS Fellow in 2015. Chris Stucchio is a product-focused data science and engineering researcher. He obtained his PhD at Rutgers University. Minh-Binh Tran is a faculty in the mathematics department of Texas A&M University, USA. He obtained a PhD in applied mathematics at Université Sorbonne Paris Nord, France. He was a recipient of the NSF CAREER Award in 2021 and was a Humboldt Fellow in 2021.

Inhalt

Introduction.- Absorbing Potentials and Perfectly Matched Layers.- Windowed Fourier Transforms and Space Phase Numerics.- Description of Time Dependent Phase Space Filters.- A More Practical Discussion: How to Choose the Parameters.- The Behavior of Gaussian Framelets under the Free Flow.- Assumptions and Accuracy Estimates.- Discussions on the Assumptions.- Proof of Theorem 7.5.6.- Proof of Theorems 7.5.4 and 7.5.5.- Numerical Experiments.