论文标题
半波图方程和calogero-moser旋转螺旋动力学的多solitons
Multi-solitons of the half-wave maps equation and Calogero-Moser spin-pole dynamics
论文作者
论文摘要
我们考虑了半波地图（HWM）方程，该方程提供了对实际线路上经典的Haldane-Shastry Spin链的连续描述。我们介绍了该方程式的确切多索顿解决方案。我们的解决方案描述了可以以不同的速度移动并以非平凡的方式相互作用的孤独激发。我们为允许任意数量的唯一数量的解决方案制作了一个安萨兹，每个唯一数量是由一个杆子中的一个描述的，并在复杂的平面中和复杂的自旋变量描述，并且我们表明，如果这些极点和旋转根据具有初始条件的某些约束的确切溶剂可溶解的旋转Calogero-Moser（CM）系统的动力学进化，则可以满足HWM方程。我们还找到了提供此自旋CM系统Bäcklund变换的一阶方程，将我们的结果推广到周期性HWM方程，并提供可视化孤子解决方案的图。
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.
