A General Scattering theory for Nonlinear and Non-autonomous Schroedinger Type Equations- A Brief description
Baoping Liu, Avy Soffer
TL;DR
This paper discusses a general scattering theory framework for nonlinear and non-autonomous Schrödinger equations, demonstrating asymptotic completeness and applicability to quantum scattering with time-dependent potentials.
Contribution
It introduces a unified approach to scattering theory for NLS-type equations with time-dependent potentials and extends the method to quantum two-body scattering.
Findings
Proves asymptotic completeness for NLS with time-dependent potentials
Extends the scattering method to quantum two-body problems
Applicable to radial data in three dimensions
Abstract
We give a short description of the proof of asymptotic-completeness for NLS-type equations, including time dependent potential terms, with radial data in three dimensions. We also show how the method applies for the two-body Quantum Scattering case.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Nonlinear Photonic Systems