{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T13:48:59Z","timestamp":1777556939742,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,30]],"date-time":"2024-12-30T00:00:00Z","timestamp":1735516800000},"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>This study presents a comprehensive investigation of cubic\u2013quartic solitons within birefringent optical fibers, focusing on the effects of the Kerr law on the refractive index. The researchers have derived soliton solutions analytically using the sine-Gordon function technique. To validate their analytical results, the study employs the improved Adomian decomposition method, a numerical technique known for its efficiency and accuracy in solving nonlinear problems. This method effectively approximates solutions while minimizing computational errors, allowing for reliable numerical simulations that corroborate the analytical findings. The insights gained from this research contribute to a deeper understanding of the symmetry properties involved in nonlinear wave propagation in optical fibers. The study highlights the significant role of nonlinearities in shaping the behavior of waves within these systems. The use of proposed method not only serves as a checking mechanism for the sine-Gordon solutions but also illustrates its potential applicability to other nonlinear systems exhibiting complex symmetry behaviors. This versatility could lead to new exploration fronts in nonlinear optics and photonics, expanding the toolkit available for researchers in these rapidly evolving fields.<\/jats:p>","DOI":"10.3390\/sym17010051","type":"journal-article","created":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T14:21:12Z","timestamp":1735654872000},"page":"51","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Numerical Validation of Certain Cubic\u2013Quartic Optical Structures Associated with the Class of Nonlinear Schr\u00f6dinger Equation"],"prefix":"10.3390","volume":"17","author":[{"given":"Afrah M.","family":"Almalki","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alyaa A.","family":"AlQarni","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Bisha, P.O. Box 551, Bisha 61922, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1403-5936","authenticated-orcid":false,"given":"Huda O.","family":"Bakodah","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3261-4667","authenticated-orcid":false,"given":"Aisha A.","family":"Alshaery","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/j.ijleo.2017.07.008","article-title":"Cubic-quartic optical solitons in Kerr and power-law media","volume":"144","author":"Biswas","year":"2017","journal-title":"Optik"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"650","DOI":"10.1016\/j.ijleo.2017.08.047","article-title":"Conservation laws for cubic-quartic optical solitons in Kerr and power-law media","volume":"145","author":"Biswas","year":"2017","journal-title":"Optik"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.ijleo.2018.05.030","article-title":"Lie symmetry analysis for cubic-quartic nonlinear Schr\u00f6dinger\u2019s equation","volume":"169","author":"Bansal","year":"2018","journal-title":"Optik"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2350235","DOI":"10.1142\/S0219887823502353","article-title":"Optical solitons of a cubic-quartic nonlinear Schr\u00f6dinger equation with parabolic law nonlinearity in optical metamaterials","volume":"20","author":"Das","year":"2023","journal-title":"Int. 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