{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T16:48:39Z","timestamp":1765212519198,"version":"3.46.0"},"reference-count":24,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,11,29]],"date-time":"2025-11-29T00:00:00Z","timestamp":1764374400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Liaoning University of Technology Doctoral Research Initiation Fund Project","award":["2312014"],"award-info":[{"award-number":["2312014"]}]},{"name":"Doctoral Research Startup Fund Project of Liaoning Provincial","award":["2025-BS-0507"],"award-info":[{"award-number":["2025-BS-0507"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper explores an innovative expansion method for solving variable-coefficient partial differential equations. Combining specific auxiliary equations with the aid of mathematical software, our method achieves notable perspectives for understanding and solving related physical problems. The validity of this method was verified through the (2+1)-dimensional variable-coefficient Burgers\u2019 equation, and the results were visualized using three-dimensional surface plots. This study proposes an effective method for solving partial differential equations that holds broad application prospects in the field of fluid physics.<\/jats:p>","DOI":"10.3390\/axioms14120882","type":"journal-article","created":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T16:41:41Z","timestamp":1765212101000},"page":"882","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Modified Auxiliary Method for Efficient Solutions to the (2+1)-Dimensional Variable-Coefficient Burgers\u2019 Equation"],"prefix":"10.3390","volume":"14","author":[{"given":"Yiman","family":"Han","sequence":"first","affiliation":[{"name":"College of Science, Liaoning University of Technology, Jinzhou 121000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6864-2822","authenticated-orcid":false,"given":"Yanni","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Science, Liaoning University of Technology, Jinzhou 121000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1515\/gmj-2022-2174","article-title":"New regularity results for the heat equation and application to non-homogeneous Burgers equation","volume":"29","author":"Benia","year":"2022","journal-title":"Georgian Math. 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