{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:01:59Z","timestamp":1760148119940,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T00:00:00Z","timestamp":1680480000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Programs of Universities in Henan Province of China","award":["22A140006","B2018-40","21IRTSTHN016","B2017-56"],"award-info":[{"award-number":["22A140006","B2018-40","21IRTSTHN016","B2017-56"]}]},{"name":"Program of Henan Polytechnic University","award":["22A140006","B2018-40","21IRTSTHN016","B2017-56"],"award-info":[{"award-number":["22A140006","B2018-40","21IRTSTHN016","B2017-56"]}]},{"name":"Innovative Scientists and Technicians Team of Henan Provincial High Education","award":["22A140006","B2018-40","21IRTSTHN016","B2017-56"],"award-info":[{"award-number":["22A140006","B2018-40","21IRTSTHN016","B2017-56"]}]},{"name":"doctoral Fund Project of Henan Polytechnic University","award":["22A140006","B2018-40","21IRTSTHN016","B2017-56"],"award-info":[{"award-number":["22A140006","B2018-40","21IRTSTHN016","B2017-56"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper outlines a study into the exact solutions of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation that is used to illustrate the ferromagnetic materials of magnetic ordering by applying two recent techniques, namely, the Sardar-subequation method and extended rational sine\u2013cosine and sinh\u2013cosh methods. Abundant exact solutions such as the bright soliton, dark soliton, combined bright\u2013dark soliton, singular soliton and other periodic wave solutions expressed by the generalized trigonometric, generalized hyperbolic, trigonometric and hyperbolic functions are obtained. The numerical results are illustrated in the form of 3D plots, 2D contours and 2D curves by choosing proper parametric values to interpret the physical behavior of the model. The obtained results in this work are expected to provide a rich platform for constructing the soliton solutions of PDEs in physics.<\/jats:p>","DOI":"10.3390\/axioms12040354","type":"journal-article","created":{"date-parts":[[2023,4,4]],"date-time":"2023-04-04T02:03:00Z","timestamp":1680573780000},"page":"354","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Various Solitons and Other Wave Solutions to the (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Dynamical Model"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6819-9464","authenticated-orcid":false,"given":"Feng","family":"Shi","sequence":"first","affiliation":[{"name":"School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3905-0844","authenticated-orcid":false,"given":"Kang-Jia","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"105939","DOI":"10.1016\/j.cnsns.2021.105939","article-title":"New general interaction solutions to the KPI equation via an optional decoupling condition approach","volume":"103","author":"Chen","year":"2021","journal-title":"Commun. 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