论文标题
拓扑分叉和行进波的重建
Topological Bifurcations and Reconstruction of Travelling Waves
论文作者
论文摘要
本文专门针对基于Virasoro组的定期行进波解决Lie-Poisson方程。我们表明，如果波浪属于统一轮廓的coadjoint轨道，则可以精确地进行任何此类解决方案的重建。同等地，相应的“流体颗粒运动”是可集成的。将此结果应用于Camassa-Holm方程，我们以参数标记周期性峰和展示轨道分叉的参数来表达颗粒的漂移：参数空间中的点数不连续变化，这反映了Virasoro Orbits拓扑的突然变化。
This paper is devoted to periodic travelling waves solving Lie-Poisson equations based on the Virasoro group. We show that the reconstruction of any such solution can be carried out exactly, regardless of the underlying Hamiltonian (which need not be quadratic), provided the wave belongs to the coadjoint orbit of a uniform profile. Equivalently, the corresponding "fluid particle motion" is integrable. Applying this result to the Camassa-Holm equation, we express the drift of particles in terms of parameters labelling periodic peakons and exhibit orbital bifurcations: points in parameter space where the drift velocity varies discontinuously, reflecting a sudden change in the topology of Virasoro orbits.
