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On the nodal structure of nonlinear stationary waves on star graphs

Band, Ram; Gnutzmann, Sven; Krueger, August


Ram Band

August Krueger


We consider stationary waves on nonlinear quantum star graphs, i.e., solutions to the stationary (cubic) nonlinear Schrödinger equation on a metric star graph with Kirchhoff matching conditions at the centre. We prove the existence of solutions that vanish at the centre of the star and classify them according to the nodal structure on each edge (i.e., the number of nodal domains or nodal points that the solution has on each edge). We discuss the relevance of these solutions in more applied settings as starting points for numerical calculations of spectral curves and put our results into the wider context of nodal counting, such as the classic Sturm oscillation theorem.


Band, R., Gnutzmann, S., & Krueger, A. (2019). On the nodal structure of nonlinear stationary waves on star graphs. Symmetry, 11(2),

Journal Article Type Article
Acceptance Date Feb 1, 2019
Online Publication Date Feb 5, 2019
Publication Date Feb 5, 2019
Deposit Date Apr 23, 2019
Publicly Available Date Apr 25, 2019
Journal Symmetry
Electronic ISSN 2073-8994
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 11
Issue 2
Article Number 185
Keywords Quantum graphs; Nonlinear Schrödinger equation; Nodal structure
Public URL
Publisher URL


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