Solitons in anharmonic chains with power-law long range interactions
S. F. Mingaleev, Yu. B. Gaididei, and F. G. Mertens,
Phys. Rev. E 58, 3833-3842 (1998).
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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 \textgreater 5 and the Benjamin-One equation for s = 4. For s \textgreater 5 the soliton tails are exponential while for 3 \textless s less than or equal to 5 they are algebraic. For s much less than 3.5 there is an energy gap between the spectra of plane waves and the soliton states.
Keywords: nonlocal interactions; thermal-conductivity; wave-propagation; atomic chains; lattices; dynamics; excitations; model
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