标题： 不稳定流形和Ginzburg-Landau涡旋的薛定谔动力学 显示英文标题

标题： Unstable manifolds and Schroedinger dynamics of Ginzburg-Landau vortices

摘要： 根据薛定谔型方程，多个相互作用的金兹堡-朗道涡旋的时间演化被近似为在有限维流形上的运动。该流形被定义为一个辅助动力系统的不稳定流形，即金兹堡-朗道能量泛函的梯度流。对于两个涡旋，相关的不稳定流形被数值构造，所诱导的动力学也被计算出来。该模型为任意涡旋分离情况下的涡旋运动提供了完整的图像，包括分离较远和几乎重合的涡旋。 显示英文摘要

摘要： The time evolution of several interacting Ginzburg-Landau vortices according to an equation of Schroedinger type is approximated by motion on a finite-dimensional manifold. That manifold is defined as an unstable manifold of an auxiliary dynamical system, namely the gradient flow of the Ginzburg-Landau energy functional. For two vortices the relevant unstable manifold is constructed numerically and the induced dynamics is computed. The resulting model provides a complete picture of the vortex motion for arbitrary vortex separation, including well-separated and nearly coincident vortices.