{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:33:08Z","timestamp":1760239988897,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,5]],"date-time":"2019-02-05T00:00:00Z","timestamp":1549324800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We consider stationary waves on nonlinear quantum star graphs, i.e., solutions to the stationary (cubic) nonlinear Schr\u00f6dinger 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.<\/jats:p>","DOI":"10.3390\/sym11020185","type":"journal-article","created":{"date-parts":[[2019,2,6]],"date-time":"2019-02-06T03:03:05Z","timestamp":1549422185000},"page":"185","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On the Nodal Structure of Nonlinear Stationary Waves on Star Graphs"],"prefix":"10.3390","volume":"11","author":[{"given":"Ram","family":"Band","sequence":"first","affiliation":[{"name":"Department of Mathematics, Technion\u2014Israel Institute of Technology, Haifa 3200003, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6925-897X","authenticated-orcid":false,"given":"Sven","family":"Gnutzmann","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"August J.","family":"Krueger","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,5]]},"reference":[{"key":"ref_1","first-page":"373","article-title":"M\u00e9moire sur une classe d\u2019\u00e9quations \u00e0 diff\u00e9rences partielles","volume":"1","author":"Sturm","year":"1836","journal-title":"J. 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