{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T16:07:18Z","timestamp":1778170038680,"version":"3.51.4"},"reference-count":53,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T00:00:00Z","timestamp":1652832000000},"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"],"award-info":[{"award-number":["22A140006"]}]},{"name":"Key Programs of Universities in Henan Province of China","award":["NSFRF210324"],"award-info":[{"award-number":["NSFRF210324"]}]},{"name":"Key Programs of Universities in Henan Province of China","award":["B2018-40"],"award-info":[{"award-number":["B2018-40"]}]},{"name":"Fundamental Research Funds for the Universities of Henan Province","award":["22A140006"],"award-info":[{"award-number":["22A140006"]}]},{"name":"Fundamental Research Funds for the Universities of Henan Province","award":["NSFRF210324"],"award-info":[{"award-number":["NSFRF210324"]}]},{"name":"Fundamental Research Funds for the Universities of Henan Province","award":["B2018-40"],"award-info":[{"award-number":["B2018-40"]}]},{"name":"Program of Henan Polytechnic University","award":["22A140006"],"award-info":[{"award-number":["22A140006"]}]},{"name":"Program of Henan Polytechnic University","award":["NSFRF210324"],"award-info":[{"award-number":["NSFRF210324"]}]},{"name":"Program of Henan Polytechnic University","award":["B2018-40"],"award-info":[{"award-number":["B2018-40"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, the integrable (2+1)-dimensional Maccari system (MS), which can model many complex phenomena in hydrodynamics, plasma physics and nonlinear optics, is investigated by the variational approach (VA). This proposed approach that based on the variational theory and Ritz-like method can construct the explicit solutions via the stationary conditions only taking two steps. Finally, the dynamic behaviors of the solutions are exhibited by choosing the appropriate parameters through the 3-D and density plots. It can be seen that the proposed method is concise and straightforward, and can be adopted to study the travelling wave theory in physics.<\/jats:p>","DOI":"10.3390\/axioms11050234","type":"journal-article","created":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T11:59:37Z","timestamp":1652875177000},"page":"234","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Investigation into the Explicit Solutions of the Integrable (2+1)\u2014Dimensional Maccari System via the Variational Approach"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3905-0844","authenticated-orcid":false,"given":"Kang-Jia","family":"Wang","sequence":"first","affiliation":[{"name":"School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Si","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":[[2022,5,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"114832","DOI":"10.1016\/j.applthermaleng.2019.114832","article-title":"A novel thermal management scheme for 3D-IC chips with multi-cores and high power density","volume":"168","author":"Ding","year":"2020","journal-title":"Appl. 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