Reply to Comment on "Existence of Internal Modes of sine-Gordon Kinks"

Abstract

In this reply to the comment by C. R. Willis, we show, by quoting his own statements, that the simulations reported in his original work with Boesch [Phys. Rev. B 42, 2290 (1990)] were done for kinks with nonzero initial velocity, in contrast to what Willis claims in his comment. We further show that his alleged proof, which assumes among other approximations that kinks are initially at rest, is not rigorous but an approximation. Moreover, there are other serious misconceptions which we discuss in our reply. As a consequence, our result that quasimodes do not exist in the sG equation [Phys. Rev. E 62, R60 (2000)] remains true.

arXiv commentReply to a comment by C. R. Willis on Phys. Rev. E 62, R60 (2000), to appear in Physical Review E

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• Resonances in the dynamics of ${\varphi }^4$ kinks perturbed by ac forces
• Anomalous resonance phenomena of solitary waves with internal modes
• On the existence of internal modes of sine-Gordon kinks
• Soliton Ratchets Induced by Excitation of Internal Modes
• Anomalies of ac driven solitary waves with internal modes: Nonparametric resonances induced by parametric forces

Cited by in corpus (1)

• Wobbles and other kink-breather solutions of the Sine Gordon model