We propose and analyze a system of nonlinear partial differential equations describing the motion of a pair of vortex filaments. Furthermore, for a pair of coaxial circular vortex filaments, we derive a condition for leapfrogging to occur and prove that the condition is necessary and sufficient for the occurrence of leapfrogging.

中文翻译：

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关于跳跃对圆涡丝的存在

我们提出并分析了描述一对涡旋丝运动的非线性偏微分方程组。进而，对于一对同轴的圆形涡流丝，我们推导出了越级发生的条件，并证明了该条件是越级发生的充分必要条件。