Multi-solitons of the half-wave maps equation and Calogero-Moser spin-pole dynamics
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.
Keywords
Cite
@article{arxiv.2006.16826,
title = {Multi-solitons of the half-wave maps equation and Calogero-Moser spin-pole dynamics},
author = {Bjorn K. Berntson and Rob Klabbers and Edwin Langmann},
journal= {arXiv preprint arXiv:2006.16826},
year = {2021}
}
Comments
32 pages, 5 figures