{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:45:13Z","timestamp":1760233513110,"version":"build-2065373602"},"reference-count":94,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,26]],"date-time":"2021-01-26T00:00:00Z","timestamp":1611619200000},"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>Systems of coupled nonlinear PDEs are applied in many fields as suitable models for many natural and physical phenomena. This makes them active and attractive subjects for both theoretical and numerical investigations. In the present paper, a symmetric nonlinear Schr\u00f6dinger (NLS) system is considered for the existence of the steady state solutions by applying a minimizing problem on some modified Nehari manifold. The nonlinear part is a mixture of cubic and superlinear nonlinearities and cubic correlations. Some numerical simulations are also illustrated graphically to confirm the theoretical results.<\/jats:p>","DOI":"10.3390\/sym13020190","type":"journal-article","created":{"date-parts":[[2021,1,26]],"date-time":"2021-01-26T00:38:16Z","timestamp":1611621496000},"page":"190","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Synchronous Steady State Solutions of a Symmetric Mixed Cubic-Superlinear Schr\u00f6dinger System"],"prefix":"10.3390","volume":"13","author":[{"given":"Riadh","family":"Chteoui","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Tabuk, Tabuk 71491, Saudi Arabia"},{"name":"Laboratory of Algebra, Number Theory and Nonlinear Analysis, Department of Mathematics, Faculty of Sciences, University of Monastir, Avenue of the Environment, Monastir 5019, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9758-5591","authenticated-orcid":false,"given":"Abdulrahman F.","family":"Aljohani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Tabuk, Tabuk 71491, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2571-1066","authenticated-orcid":false,"given":"Anouar","family":"Ben Mabrouk","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, University of Tabuk, Tabuk 71491, Saudi Arabia"},{"name":"Laboratory of Algebra, Number Theory and Nonlinear Analysis, Department of Mathematics, Faculty of Sciences, University of Monastir, Avenue of the Environment, Monastir 5019, Tunisia"},{"name":"Department of Mathematics, Higher Institute of Applied Mathematics and Computer Science, University of Kairouan, Street of Assad Ibn Alfourat, Kairouan 3100, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3454","DOI":"10.3923\/jas.2011.3454.3463","article-title":"Numerical simulation of coupled nonlinear Schr\u00f6dinger equation by RDTM and comparison with DTM","volume":"11","author":"Abazari","year":"2011","journal-title":"J. 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