Asymmetric Envelope and Hole Solitons in a Monoatomic Chain with Kac–Baker-like Long-Range Interaction Potential

Abstract

By using the quasidiscrete multiple-scale method, we study the nonlinear properties of a monoatomic chain with Kac–Baker-like long-range harmonic interaction. Besides the usual asymmetric envelope solitons, a novel nonliear elementary excitation, a hole-soliton, is analytically derived. It is found that the dispersion relation and group velocity exhibit some characters different from that of the nonlinear chain without Kac–Baker-like long-range harmonic interaction. Furthermore, these solitons are nonpropagating at other sites except for the center of Brillouin zone, and the group velocity of the soliton at the center of Brillouin zone is supersonic.