Multi-solitons of the half-wave maps equation and Calogero–Moser spin–pole dynamics
Multi-solitons of the half-wave maps equation and Calogero–Moser spin–pole dynamics
复制标题
半波映射方程的多孤子和Calogero-Moser自旋极动力学
DOI：
10.1088/1751-8121/abb167
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
E. Langmann
中科院分区：
文献类型：
--
作者：
B. Berntson;R. Klabbers;E. Langmann
我们考虑了半波映射方程，它提供了在实线上经典Haldane-Shastry自旋链的连续体描述。我们给出了该方程的精确多孤子解。我们的解描述了可以以不同速度运动并以非平凡方式相互作用的孤立自旋激发。我们对允许任意数量的孤子的解进行了分析，每个孤子由复平面上的一个极点和一个复自旋变量描述，并且我们证明了如果这些极点和自旋根据具有一定初始条件约束的精确可解自旋Calogero-Moser （CM）系统的动力学演化，则HWM方程是满足的。我们还找到了提供该自旋CM系统Bäcklund变换的一阶方程，将我们的结果推广到周期HWM方程，并提供了可视化的孤子解图。
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.
影响因子：
1.3
作者：
Chalykh, Oleg;Silantyev, Alexey
通讯作者：
Silantyev, Alexey