Fractal solutions of dispersive partial differential equations on the torus

被引：0
作者：
M. B. Erdoğan
G. Shakan
机构：
[1] University of Illinois,Department of Mathematics
来源：
Selecta Mathematica | 2019年 / 25卷
关键词：
35Q55; 11L03;
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摘要：
We use exponential sums to study the fractal dimension of the graphs of solutions to linear dispersive PDE. Our techniques apply to Schrödinger, Airy, Boussinesq, the fractional Schrödinger, and the gravity and gravity–capillary water wave equations. We also discuss applications to certain nonlinear dispersive equations. In particular, we obtain bounds for the dimension of the graph of the solution to cubic nonlinear Schrödinger and Korteweg–de Vries equations along oblique lines in space–time.
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