The superlattices of discrete breathers in the model of the 1D crystal

Abstract

The dynamics of the discrete breather superlattices in the model of the 1D anharmonic Hirota lattice is considered. The analogues of the discrete breather for the finite-size system with periodic boundary conditions are presented. For the analogue of the discrete breather for the finite-size system the stability and the effect of dissipation on the dynamics are discussed. Using the exact solutions of the Hirota lattice equation in the form of discrete breather superlattices the asymptotic interaction energy between two breathers is investigated. It is shown that for the considered parameters of the solutions discrete breathers in the superlattice of type I repel, while in the superlattice of type II attract each other.