Abstract
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 Bäcklund transformation of this spin CM system, generalize our results to the periodic HWM equation, and provide plots that visualize our soliton solutions.
Funder
Göran Gustafsson Foundation
Swedish Research Council
Stiftelse Olle Engkvist Byggmästare
H2020 European Research Council
Knut och Alice Wallenbergs Stiftelse
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
11 articles.
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