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

Author:

Berntson Bjorn KORCID,Klabbers RobORCID,Langmann EdwinORCID

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

Publisher

IOP Publishing

Subject

General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics

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