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Classical solitons for a one-dimensional many-body system with inverse-square interaction.

We investigate solitons in the one-dimensional classical many-body system of particles interacting by an inverse-square pair potential. We use a combination of numerical results for finite systems, and exact results for the continuum limit, to deduce properties of solitons in the thermodynamic limit. Two remarkable conjectures are supported by these results, and the correspondence with the exact results for the quantum system is established.