TY - JOUR
T1 - Curvature effects on spiral spectra
T2 - Generation of point eigenvalues near branch points
AU - Sandstede, Björn
AU - Scheel, Arnd
PY - 2006/1
Y1 - 2006/1
N2 - It is shown that spiral waves may possess many isolated point eigenvalues that appear near branch points of the linear dispersion relation. These eigenvalues are created by the same mechanism that leads to infinitely many bound states for selfadjoint Schrödinger operators with sufficiently weakly decaying long-range potentials. For spirals, the weak decay of the potential is due to the curvature effects on the profile of the spiral in an intermediate spatial range that separates the spiral core from the far field.
AB - It is shown that spiral waves may possess many isolated point eigenvalues that appear near branch points of the linear dispersion relation. These eigenvalues are created by the same mechanism that leads to infinitely many bound states for selfadjoint Schrödinger operators with sufficiently weakly decaying long-range potentials. For spirals, the weak decay of the potential is due to the curvature effects on the profile of the spiral in an intermediate spatial range that separates the spiral core from the far field.
UR - http://www.scopus.com/inward/record.url?scp=32844455300&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=32844455300&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.73.016217
DO - 10.1103/PhysRevE.73.016217
M3 - Article
AN - SCOPUS:32844455300
SN - 1539-3755
VL - 73
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 1
M1 - 016217
ER -