Solitons in a continuous classical Haldane-Shastry spin chain

Abstract

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.

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Cited by in corpus (10)

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• The non-chiral intermediate Heisenberg ferromagnet equation
• Integrability, conservation laws and solitons of a many-body dynamical system associated with the half-wave maps equation
• Global Well-Posedness For Half-Wave Maps With $S^2$ and ${\mathbb{H}}^2$ Targets For Small Smooth Initial Data
• Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation
• Global Well-Posedness and Soliton Resolution for the Half-Wave Maps Equation with Rational Data
• Periodic solutions of the non-chiral intermediate Heisenberg ferromagnet equation described by elliptic spin Calogero-Moser dynamics