Orbital Stability of Periodic Standing Waves for the Logarithmic Klein-Gordon Equation

TL;DR

This paper establishes the orbital stability of periodic standing waves in the one-dimensional logarithmic Klein-Gordon equation, using advanced analytical techniques to prove existence, uniqueness, and stability of solutions.

Contribution

It introduces a novel stability analysis for periodic standing waves in the logarithmic Klein-Gordon equation, combining compactness and non-standard analysis methods.

Findings

Existence and uniqueness of weak solutions in the energy space.

Orbital stability of periodic standing waves proven.

Application of non-standard analysis techniques.

Abstract

The main goal of this paper is to present orbital stability results of periodic standing waves for the one-dimensional logarithmic Klein-Gordon equation. To do so, we first use compactness arguments and a non-standard analysis to obtain the existence and uniqueness of weak solutions for the associated Cauchy problem in the energy space. Second, we prove the orbital stability of standing waves using a stablity analysis of conservative systems.