Abstract: 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>5 and the Benjamin-One equation for s = 4. For s>5 the soliton tails are exponential while for 3

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