{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T06:34:36Z","timestamp":1775630076444,"version":"3.50.1"},"reference-count":58,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,10]],"date-time":"2022-11-10T00:00:00Z","timestamp":1668038400000},"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 work recovers cubic-quartic optical solitons with dispersive reflectivity in fiber Bragg gratings and parabolic law of nonlinearity. The Lie symmetry analysis first reduces the governing partial differential equations to the corresponding ordinary differential equations which are subsequently integrated. This integration is conducted using two approaches which are the modified Kudryashov\u2019s approach as well as the generalized Arnous\u2019 scheme. These collectively yielded a full spectrum of cubic-quartic optical solitons that have been proposed to control the depletion of the much-needed chromatic dispersion. They range from bright, dark, singular to combo solitons. These solitons are considered with dispersive reflectivity, which maintains the necessary balance between chromatic dispersion and nonlinear refractive index structure for an uninterrupted transmission of solitons along intercontinental distances. Their respective surface and contour plots are also exhibited. A few closing words are included with some prospective future avenues of research to extend this topic further.<\/jats:p>","DOI":"10.3390\/sym14112370","type":"journal-article","created":{"date-parts":[[2022,11,10]],"date-time":"2022-11-10T19:18:29Z","timestamp":1668107909000},"page":"2370","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Cubic-Quartic Optical Solitons in Fiber Bragg Gratings with Dispersive Reflectivity Having Parabolic Law of Nonlinear Refractive Index by Lie Symmetry"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1236-2941","authenticated-orcid":false,"given":"Sandeep","family":"Malik","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Central University of Punjab, Bathinda 151401, Punjab, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6883-7788","authenticated-orcid":false,"given":"Sachin","family":"Kumar","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Central University of Punjab, Bathinda 151401, Punjab, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anjan","family":"Biswas","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245, USA"},{"name":"Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia"},{"name":"Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Hwy, 115409 Moscow, Russia"},{"name":"Department of Applied Sciences, Cross\u2013Border Faculty, Dunarea de Jos University of Galati, 111 Domneasca Street, 800201 Galati, Romania"},{"name":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yakup","family":"Y\u0131ld\u0131r\u0131m","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Biruni University, Istanbul 34010, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9121-5714","authenticated-orcid":false,"given":"Luminita","family":"Moraru","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Physics and Environment, Faculty of Sciences and Environment, Dunarea de Jos University of Galati, 47 Domneasca Street, 800008 Galati, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5934-329X","authenticated-orcid":false,"given":"Simona","family":"Moldovanu","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Information Technology, Faculty of Automation, Computers, Electrical Engineering and Electronics, Dunarea de Jos University of Galati, 47 Domneasca Street, 800008 Galati, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8350-9424","authenticated-orcid":false,"given":"Catalina","family":"Iticescu","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Physics and Environment, Faculty of Sciences and Environment, Dunarea de Jos University of Galati, 47 Domneasca Street, 800008 Galati, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hashim M.","family":"Alshehri","sequence":"additional","affiliation":[{"name":"Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"11925","DOI":"10.1016\/j.aej.2022.05.042","article-title":"Bright solitons for twin-core couplers and multiple-core couplers having polynomial law of nonlinearity using Jacobi elliptic function expansion method","volume":"61","author":"Khalil","year":"2022","journal-title":"Alex. 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