WAVES ALONG FRACTAL COASTLINES: FROM FRACTAL ARITHMETIC TO WAVE EQUATIONS

被引：29
作者：
Czachor, Marek [1 ]
机构：
[1] Gdansk Univ Technol, Dept Theoret Phys & Quantum Informat, G Narutowicza 11-12, PL-80233 Gdansk, Poland
来源：
ACTA PHYSICA POLONICA B | 2019年 / 50卷 / 04期
关键词：
CALCULUS; CURVES;
D O I：
10.5506/APhysPolB.50.813
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Beginning with addition and multiplication intrinsic to a Koch-type curve, we formulate and solve wave equation describing wave propagation along a fractal coastline. As opposed to examples known from the literature, we do not replace the fractal by the continuum in which it is embedded. This seems to be the first example of a truly intrinsic description of wave propagation along a fractal curve. The theory is relativistically covariant under an appropriately defined Lorentz group.
引用
收藏
页码：813 / 831
页数：19
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