Solitons in anharmonic chains with power-law long-range interactions

We study the influence of long-range interactions with distance dependence $r^{-s}$ of the elastic coupling constant on the properties of pulse solitons in a one-dimensional anharmonic chain. Introducing the approximations of small amplitude and long wavelength, we have arrived at the Boussinesq equation for $s>\mathrm{}5\mathrm{}$ and the Benjamin-Ono equation for $s=4.\mathrm{}$ For $s>\mathrm{}5\mathrm{}$ the soliton tails are exponential while for $3<s<~5$ they are algebraic. For $s<~3.5$ there is an energy gap between the spectra of plane waves and the soliton states.