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

@article{Berntson2020MultisolitonsOT, title={Multi-solitons of the half-wave maps equation and Calogero–Moser spin–pole dynamics}, author={Bjorn K Berntson and Rob Klabbers and Edwin Langmann}, journal={Journal of Physics A}, year={2020}, volume={53}, pages={505702} }

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…

## 4 Citations

Derivation of the Half-Wave Maps Equation from Calogero--Moser Spin Systems

- Physics, Mathematics
- 2020

We prove that the energy-critical half-wave maps equation \[ \partial_t \mathbf{S} =\mathbf{S} \times |\nabla| \mathbf{S}, \quad (t,x) \in \mathbb{R} \times \mathbb{T} \] arises as an effective…

Global Well-Posedness For Half-Wave Maps With $S^2$ and $\mathbb{H}^2$ Targets For Small Smooth Initial Data

- Mathematics
- 2021

We prove global well-posedness for the half-wave map with S target for small Ḣ n 2 × Ḣ n 2 −1 initial data. We also prove the global well-posedness for the equation with H 2 target for small smooth Ḃ…

Integrability, conservation laws and solitons of a many-body dynamical system associated with the half-wave maps equation

- Physics, MathematicsPhysica D: Nonlinear Phenomena
- 2021

How coordinate Bethe ansatz works for Inozemtsev model

- Physics, Mathematics
- 2020

Three decades ago, Inozemtsev found an isotropic long-range spin chain with elliptic pair potential that interpolates between the Heisenberg and Haldane-Shastry (HS) spin chains while admitting an…

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