Can low-frequency breathers exist in a quasi-1D crystal?

Abstract

We investigate a quasi-1D crystal: 2D system of coupled linear chains of particles with strong intra-chain and weak inter-chain interactions. Nonlinear dynamics of one of these chains when the rest of them are fixed is reduced to the well known Frenkel-Kontorova (FK) model. Its continuum limit, sine-Gordon (sG) equation, predicts two types of soliton solutions: topological solitons and breathers. It is known that the quasi-1D topological solitons exist also in a 2D system of coupled chains and even in a 3D model of a polymer crystal. Numerical simulation shows that the breathers inherent to the FK model do not exist in the system of chains. The effect changes scenario of kink-antikink collision at small velocities: it always results only in intensive phonon radiation while kink-antikink recombination in the FK model results in long-living low-frequency sG breather creation. The reason of the difference is that the model of coupled chains catches 'acoustic' part of phonon spectrum of a crystal while the FK model does not. Low-frequency SG breathers in a crystal intensively emit resonant 'acoustic' phonons and come to ruin.