On the radius of spatial analyticity for the Klein-Gordon-Schr\"{o}dinger system

TL;DR

This paper investigates how the spatial analyticity radius of solutions to the non-relativistic Klein-Gordon-Schrödinger system persists over time, establishing an algebraic lower bound as time approaches infinity.

Contribution

It provides the first analysis of the spatial analyticity persistence for coupled nonlinear dispersive systems in the non-relativistic regime.

Findings

The radius of spatial analyticity has an algebraic lower bound over time.

Results extend understanding from single equations to coupled systems.

Analysis is specific to the non-relativistic Klein-Gordon-Schrödinger system.

Abstract

In this paper, we study the persistence of spatial analyticity for the solutions to the Klein-Gordon-Schr\"{o}dinger system, which describes a physical system of a nucleon field interacting with a neutral meson field, with analytic initial data. Unlike the case of a single nonlinear dispersive equation, not much is known about nonlinear dispersive systems as it is harder to show the spatial analyticity of coupled equations simultaneously. The only results known so far are rather recent ones for the Dirac-Klein-Gordon system which governs the physical system when the nucleon is described by Dirac spinor fields in the case of relativistic fields. In contrast, we aim here to study the Klein-Gordon-Schr\"{o}dinger system that works in the non-relativistic regime. It is shown that the radius of spatial analyticity of the solutions at later times obeys an algebraic lower bound as time goes to infinity.