论文标题
实验性观察沿流体圆环的周期性korteweg-de vries soliton
Experimental observation of periodic Korteweg-de Vries solitons along a torus of fluid
论文作者
论文摘要
我们报告了沿流体圆环传播的孤子的实验观察。我们表明，与经典平面几何形状相比，这种周期系统会导致显着差异。特别是，我们强调了亚音速守平孔的观察，以及孤子速度对其振幅的非线性依赖性。使用高分辨率的时空测量值对孤子轮廓，速度，碰撞和耗散进行了表征。通过将周期性的边界条件施加到Korteweg-de Vries（KDV）方程式上，我们恢复了这些观察结果。在此周期性的几何形状中，还实施了孤子子的非线性光谱分析（周期性反向散射变换）。因此，我们的工作揭示了周期性对研究孤子的重要性，并且可以应用于涉及由KDV方程支配的周期系统的其他领域。
We report on the experimental observation of solitons propagating along a torus of fluid. We show that such a periodic system leads to significant differences compared to the classical plane geometry. In particular, we highlight the observation of subsonic elevation solitons, and a nonlinear dependence of the soliton velocity on its amplitude. The soliton profile, velocity, collision, and dissipation are characterized using high resolution space-time measurements. By imposing periodic boundary conditions onto Korteweg-de Vries (KdV) equation, we recover these observations. A nonlinear spectral analysis of solitons (periodic inverse scattering transform) is also implemented and experimentally validated in this periodic geometry. Our work thus reveals the importance of periodicity for studying solitons and could be applied to other fields involving periodic systems governed by a KdV equation.
