Solitons in a continuous classical Haldane–Shastry spin chain

•We construct a classical version of continuum Haldane–Shastry model and analyze its classical dynamics.•We have obtained analytic multi-lump solitary wave solutions for our spin-field equation.•Our numerical collision experiments suggest the existence of true multi-soliton solutions.

Motivated by Polychronakos' discovery that solitons exist in the hydrodynamic equations of continuum version of the Calogero model, we seek solitons in the classical dynamics of a continuum version of the Haldane–Shastry spin chain. We have obtained analytic multi-lump solitary wave solutions for our spin-field equation, and these solutions possess interesting topological features. We have performed numerical collision experiments showing that the solitary waves survive collisions, and thus suggest the existence of true multi-soliton solutions.