Nonequivalence of phonon modes in the sine-Gordon equation

Abstract

We study the resonances in the sine-Gordon equation driven by an ac force using a linear perturbation theory. We show that resonances take place when the driving frequency d is equal to half of the phonon modes’ frequencies as has been shown numerically in our earlier work [ N. R. Quintero, A. Sanchez, and F. G. Mertens, Phys. Rev. E 62 , R60 ( 2000)] , however, we find that the ac force is able to excite not all the phonon modes, but rather only the odd phonons ( i.e., the ones with odd eigenfunctions)