可积系统系列报告：Higher-dimensional Dispersive Quantization

讲座时间 Datetime: 2021年5月25日，星期二 15:00-16:30

地点 Venue: 腾讯会议，996 682 270

报告人 Speaker: 康静 教授

单位 Affiliation: 西北大学

报告摘要 Abstract: 

  In this talk, we investigate the dispersive quantization of the two-dimensional linear dispersive equations subject to the periodic initial-boundary value problem over a bounded domain on the plane. We first study the periodic initial-boundary value problem for the two-dimensional linear KdV equation on a rectangle domain. We show that the piecewise constant initial data leads to quantized structures at rational times, meaning that the solution is piecewise constant on rational sub-rectangle. Furthermore, we verify these results extend to general two-dimensional linear dispersive equations with “integral polynomial” dispersion relations, subject to a more general piecewise smooth initial condition. The solution is a linear combination of finitely many translates of the initial data. Finally, we study the fractal structure of the solutions at irrational times.