Stability and instability of radial standing waves to NLKG equation with an inverse-square potential

TL;DR

This paper investigates the stability and instability of radial standing waves in a nonlinear Klein-Gordon equation with an inverse-square potential, focusing on the properties of the radial ground state solutions.

Contribution

It provides new insights into the stability behavior of radial ground states under the influence of an inverse-square potential in the NLKG equation.

Findings

Radial ground states exhibit both stability and instability depending on parameters.

The inverse-square potential significantly affects the stability properties of standing waves.

The study advances understanding of wave behavior in singular potential settings.

Abstract

In this paper, we consider radial standing waves to a nonlinear Klein-Gordon equation with a repulsive inverse-square potential. It is known that existence of a "radial" ground state to the stationary problem of the nonlinear Klein-Gordon equation. Here, the "radial" ground state is a solution with the least energy among radial solutions to the stationary problem. We deal with stability and instability of the standing wave for the "radial" ground state.