We study the influence of long-range interatomic interactions on the proper
ties of supersonic pulse solitons in anharmonic chains. We show that in the
case of ultra-long-range (e.g., screened Coulomb) interactions three diffe
rent types of pulse solitons coexist in a certain velocity interval: one ty
pe is unstable but the two others are stable. The high-energy stable solito
n is broad and can be described in the quasicontinuum approximation. But th
e low-energy stable soliton consists of two components, short-range and lon
g-range ones, and can be considered as a bound state of these components.