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 paper. 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 paper. As a consequence, our result that quasimodes do not exist in the sG equation [Phys. Rev. E 62, R60 (2000)] remains true.