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arXiv · 2006.16826

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

Bjorn K. Berntson·Rob Klabbers·Edwin Langmann
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Abstract

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

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BibTeXRIS

Bjorn K. Berntson, Rob Klabbers, Edwin Langmann. 2020-06-30. Multi-solitons of the half-wave maps equation and Calogero-Moser spin-pole dynamics. https://doi.org/10.1088/1751-8121%2Fabb167

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