Curvature effects on spiral spectra: Generation of point eigenvalues near branch points

Björn Sandstede, Arnd Scheel

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

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.

Original languageEnglish (US)
Article number016217
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume73
Issue number1
DOIs
StatePublished - Jan 2006

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