Solitons in anharmonic chains with long-range interactions

Abstract

The authors study the influence of long-range atomic interactions on the properties of soliton-like excitations in a one-dimensional anharmonic chain. In the continuum approximation supersonic and subsonic kink pulse soliton solutions are found that can coexist in the lattice. The corresponding velocity domains are separated by a gap that depends on the range of the interaction. The modulated-wave solutions are investigated in the weakly non-linear case and the small-wavevector limit. A possible alternation of envelope and dark solitons is found that can exist for both cooperative and competitive short- and long-range interactions.