Abstract
We investigate the points of constancy in the piecewise constant solution profiles of the periodic linearized Korteweg–deVries equation with step function initial data at rational times. The solution formulae are given by certain Weyl sums, and we employ number theoretic techniques, including Kummer sums, in our analysis. These results constitute an initial attempt to understand the complementary phenomenon of ‘fractalization’ at irrational times.
| Original language | English (US) |
|---|---|
| Article number | 0160 |
| Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 474 |
| Issue number | 2217 |
| DOIs | |
| State | Published - Sep 1 2018 |
Bibliographical note
Publisher Copyright:© 2018 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License.
Keywords
- Dispersive quantization
- Kummer sum
- Linearized Korteweg–deVries equation
- Point of constancy
- Weyl sum