{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:22:01Z","timestamp":1760145721117,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,8,26]],"date-time":"2024-08-26T00:00:00Z","timestamp":1724630400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11805114","1197050803","2018TDJH101"],"award-info":[{"award-number":["11805114","1197050803","2018TDJH101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"SDUST Research Fund","award":["11805114","1197050803","2018TDJH101"],"award-info":[{"award-number":["11805114","1197050803","2018TDJH101"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this article, the coupled Kundu equations are analyzed using the Fokas unified method on the half-line. We resolve a Riemann\u2013Hilbert (RH) problem in order to illustrate the representation of the potential function in the coupled Kundu equations. The jump matrix is obtained from the spectral matrix, which is determined according to the initial value data and the boundary value data. The findings indicate that these spectral functions exhibit interdependence rather than being mutually independent, and adhere to a global relation while being connected by a compatibility condition.<\/jats:p>","DOI":"10.3390\/axioms13090579","type":"journal-article","created":{"date-parts":[[2024,8,26]],"date-time":"2024-08-26T07:53:37Z","timestamp":1724658817000},"page":"579","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Initial Boundary Value Problem for the Coupled Kundu Equations on the Half-Line"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-3284-0965","authenticated-orcid":false,"given":"Jiawei","family":"Hu","sequence":"first","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"}]},{"given":"Ning","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"},{"name":"Department of Fundamental Course, Shandong University of Science and Technology, Taian 271019, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1002\/cpa.3160270108","article-title":"The Korteweg-de Vries Equation and Generalizations. 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