Existence of internal modes of sine-Gordon kinks

Abstract

We study whether or not sine-Gordon kinks exhibit internal modes or ‘‘quasimodes.’’ By considering the response of the kinks to ac forces and initial distortions, we show that neither intrinsic internal modes nor ‘‘quasimodes’’ exist in contrast to previous reports. However, we do identify a different kind of internal mode bifurcating from the bottom edge of the phonon band which arises from the discretization of the system in the numerical simulations, thus confirming recent predictions.