An Envelope Soliton in a Nonlinear Chain with the Power-Law Dependence of Long-Range Interaction

We study the Fermi-Pasta-Ulam lattice model in the presence of a power-law dependence of long-range interaction by virtue of the method of multiple scales. Our results show that an envelope soliton still appears, but it is of different property for the group velocity compared with that of the soliton in the model when long-range interaction is absent.