@inbook{08695cc5a4d849c0bfd474f02ce02995,
title = "Nonlinear sturm oscillation: From the interval to a star",
abstract = "The Sturm oscillation property, i.e. that the n-th eigenfunction of a Sturm-Liouville operator on an interval has n − 1 zeros (nodes), has been well studied. This result is known to hold when the interval is replaced by a metric (quantum) tree graph. We prove that the solutions of the real stationary nonlinear Schr{\"o}dinger equation on an interval satisfy a nonlinear version of the Sturm oscillation property. However, we show that unlike for the linear theory, the nonlinear version of Sturm oscillation breaks down already for a star graph. We point out conditions under which this violation can be assured.",
keywords = "Nonlinear schr{\"o}dinger equation, Quantum graph, Spectral curve, Sturm oscillation",
author = "Ram Band and Krueger, {August J.}",
note = "Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",
year = "2018",
doi = "10.1090/conm/717/14445",
language = "الإنجليزيّة",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "129--154",
booktitle = "Contemporary Mathematics",
address = "الولايات المتّحدة",
}