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

• 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 Backlund transformation of this spin CM system, generalize our results to the periodic HWM equation, and provide plots that visualize our soliton solutions.

Subject headings

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Keyword

hydrodynamics

integrable system

solitons

spin Calogero&#8211

Moser system

Publication and Content Type

ref (subject category)

art (subject category)