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Multi-solitons of the half-wave maps equation and Calogero-Moser spin-pole dynamics
- Source :
- J. Phys. A: Math. Theor. 53, 505702 (2020)
- Publication Year :
- 2020
-
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.<br />Comment: 32 pages, 5 figures
Details
- Database :
- arXiv
- Journal :
- J. Phys. A: Math. Theor. 53, 505702 (2020)
- Publication Type :
- Report
- Accession number :
- edsarx.2006.16826
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1088/1751-8121/abb167