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We consider the half-wave maps (HWM) equation which provides a continuumdescription of the classical Haldane-Shastry spin chain on the real line. Wepresent exact multi-soliton solutions of this equation. Our solutions describesolitary spin excitations that can move with different velocities and interactin a non-trivial way. We make an ansatz for the solution allowing for anarbitrary number of solitons, each described by a pole in the complex plane anda complex spin variable, and we show that the HWM equation is satisfied ifthese poles and spins evolve according to the dynamics of an exactly solvablespin Calogero-Moser (CM) system with certain constraints on initial conditions.We also find first order equations providing a B\"acklund transformation ofthis spin CM system, generalize our results to the periodic HWM equation, andprovide plots that visualize our soliton solutions.

Multi-solitons of the half-wave maps equation and Calogero-Moser spin-pole dynamics