On nonlinear wave equations with parabolic potentials

TL;DR

This paper introduces a new class of piece-wise quadratic potentials for nonlinear wave equations, enabling exact spectral analysis of linearized operators at kink solutions, which is crucial for stability studies.

Contribution

The paper presents a novel class of potentials that allow explicit spectral characterization of linearized operators around kinks, advancing stability analysis methods.

Findings

Exact spectral descriptions for linearized operators at kinks

New class of piece-wise quadratic potentials introduced

Facilitates stability analysis of nonlinear wave kinks

Abstract

We introduce a new class of piece-wise quadratic potentials for nonlinear wave equations with a kink solutions. The potentials allow an exact description of the spectral properties for the linearized equation at the kink. This description is necessary for the study of the stability properties of the kinks.