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Multi-solitons of t...
Multi-solitons of the half-wave maps equation and Calogero-Moser spin-pole dynamics
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- Berntson, Bjorn K. (author)
- KTH,Matematik (Inst.)
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- Klabbers, Rob (author)
- Stockholms universitet,KTH,Nordic Institute for Theoretical Physics NORDITA,;Stockholm Univ, SE-10691 Stockholm, Sweden.,Nordiska institutet för teoretisk fysik (Nordita)
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- Langmann, Edwin (author)
- KTH,Kondenserade materiens teori
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KTH Matematik (Inst) (creator_code:org_t)
- 2020-11-23
- 2020
- English.
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In: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 53:50
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Abstract
Subject headings
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- 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–
- Moser system
Publication and Content Type
- ref (subject category)
- art (subject category)
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