{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,15]],"date-time":"2026-02-15T08:43:40Z","timestamp":1771145020596,"version":"3.50.1"},"reference-count":18,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,24]],"date-time":"2019-03-24T00:00:00Z","timestamp":1553385600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["Fractal grid"],"award-info":[{"award-number":["Fractal grid"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004794","name":"Centre National de la Recherche Scientifique","doi-asserted-by":"publisher","award":["PEPS InPhyNiTi \u201cFARA\u201d"],"award-info":[{"award-number":["PEPS InPhyNiTi \u201cFARA\u201d"]}],"id":[{"id":"10.13039\/501100004794","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We considered the propagation of nonlinear shallow water waves in a narrow channel presenting a fork. We aimed at computing the coupling conditions for a 1D effective model, using 2D simulations and an analysis based on the conservation laws. For small amplitudes, this analysis justifies the well-known Stoker interface conditions, so that the coupling does not depend on the angle of the fork. We also find this in the numerical solution. Large amplitude solutions in a symmetric fork also tend to follow Stoker\u2019s relations, due to the symmetry constraint. For non symmetric forks, 2D effects dominate so that it is necessary to understand the flow inside the fork. However, even then, conservation laws give some insight in the dynamics.<\/jats:p>","DOI":"10.3390\/sym11030434","type":"journal-article","created":{"date-parts":[[2019,3,25]],"date-time":"2019-03-25T06:56:52Z","timestamp":1553497012000},"page":"434","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Coupling Conditions for Water Waves at Forks"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8291-6722","authenticated-orcid":false,"given":"Jean\u2013Guy","family":"Caputo","sequence":"first","affiliation":[{"name":"Laboratoire de Math\u00e9matiques, INSA Rouen Normandie, 76801 Saint\u2013Etienne du Rouvray, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5247-2788","authenticated-orcid":false,"given":"Denys","family":"Dutykh","sequence":"additional","affiliation":[{"name":"University Grenoble Alpes, University Savoie Mont Blanc, CNRS, LAMA, 73000 Chamb\u00e9ry, France"}]},{"given":"Bernard","family":"Gleyse","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matiques, INSA Rouen Normandie, 76801 Saint\u2013Etienne du Rouvray, France"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"47","DOI":"10.4171\/emss\/2","article-title":"Flows on networks: Recent results and perspectives","volume":"1","author":"Bressan","year":"2014","journal-title":"EMS Surv. 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