TY - JOUR
T1 - Dispersive quantization
AU - Olver, Peter J.
PY - 2010/8
Y1 - 2010/8
N2 - The evolution, through linear dispersion, of piecewise constant periodic initial data leads to surprising quantized structures at rational times, and fractal, nondifferentiable profiles at irrational times. Similar phenomena have been observed in optics and quantum mechanics, and lead to intriguing connections with exponential sums arising in number theory. Ramifications of these observations for numerics and nonlinear dispersion are proposed as open problems.
AB - The evolution, through linear dispersion, of piecewise constant periodic initial data leads to surprising quantized structures at rational times, and fractal, nondifferentiable profiles at irrational times. Similar phenomena have been observed in optics and quantum mechanics, and lead to intriguing connections with exponential sums arising in number theory. Ramifications of these observations for numerics and nonlinear dispersion are proposed as open problems.
UR - http://www.scopus.com/inward/record.url?scp=77956157433&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77956157433&partnerID=8YFLogxK
U2 - 10.4169/000298910X496723
DO - 10.4169/000298910X496723
M3 - Article
AN - SCOPUS:77956157433
SN - 0002-9890
VL - 117
SP - 599
EP - 610
JO - American Mathematical Monthly
JF - American Mathematical Monthly
IS - 7
ER -