Points of constancy of the periodic linearized Korteweg–deVries equation
| Autor: | Efstratios Tsatis, Peter J. Olver |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
High Energy Physics - Theory
Mathematics - Number Theory General Mathematics 010102 general mathematics Kummer sum Mathematical analysis General Engineering FOS: Physical sciences General Physics and Astronomy 01 natural sciences 35Q53 11L03 11L15 28A80 Mathematics - Analysis of PDEs High Energy Physics - Theory (hep-th) Step function Irrational number 0103 physical sciences FOS: Mathematics Piecewise Number Theory (math.NT) 0101 mathematics 010306 general physics Constant (mathematics) Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 474:20180160 |
| ISSN: | 1471-2946 1364-5021 |
| DOI: | 10.1098/rspa.2018.0160 |
| Popis: | 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 formulas 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 phenomenon of "fractalization" observed at irrational times. Comment: Published version |
| Databáze: | OpenAIRE |
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