Refined Scattering and Hermitian Spectral Theory for Linear Higher-Order Schr\"odinger Equations

TL;DR

This paper classifies the long-term and finite-time blow-up behaviors of solutions to higher-order Schrödinger equations, providing insights into their asymptotic properties.

Contribution

It introduces a refined scattering and Hermitian spectral theory tailored for linear higher-order Schrödinger equations, advancing understanding of their solution behaviors.

Findings

Classification of large-time asymptotics

Finite-time blow-up analysis

Development of spectral theory for higher-order equations

Abstract

A classification of large-time and finite-time blow-up asymptotics of solutions of the Cauchy problem for higher-order Schr\"odinger equations is performed.