On dispersion for Klein Gordon equation with periodic potential in 1D
Scipio Cuccagna
TL;DR
This paper establishes decay estimates for the Klein-Gordon equation with a periodic potential in one dimension, leveraging Bloch function estimates to understand wave dispersion in such structured media.
Contribution
It introduces new decay estimates for the Klein-Gordon equation with periodic potentials, extending previous Bloch function analysis to time-dependent wave behavior.
Findings
Decay estimates for Klein-Gordon with periodic potential
Application of Bloch function estimates in 1D
Enhanced understanding of wave dispersion in periodic media
Abstract
By exploiting estimates on Bloch functions obtained in a previous paper, we prove decay estimates for Klein Gordon equations with a time independent potential periodic in space in 1D and with generic mass
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Quantum chaos and dynamical systems · Nonlinear Photonic Systems