Solitons in a continuous classical Haldane-Shastry spin chain

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 these solitary waves survive collisions, and thus suggest the existence of true multi-soliton solutions.