{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:13:27Z","timestamp":1760058807787,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,27]],"date-time":"2025-04-27T00:00:00Z","timestamp":1745712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science and Technology Program of Guangzhou","award":["2023A04J1325"],"award-info":[{"award-number":["2023A04J1325"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we investigate closed-form meromorphic solutions of the fifth-order Sawada-Kotera (fSK) equation and (3+1)-dimensional generalized shallow water (gSW) equation. The study of high-order and high-dimensional differential equations is pivotal for modeling complex nonlinear phenomena in physics and engineering, where higher-order dispersion, dissipation, and multidimensional dynamics govern system behavior. Constructing explicit solutions is of great significance for the study of these equations. The elliptic, hyperbolic, rational, and exponential function solutions for these high-order and high-dimensional differential equations are achieved by proposing the extended complex method. The planar dynamics behavior of the (3+1)-dimensional gSW equation and its phase portraits are analyzed. Using computational simulation, the chaos behaviors of the high-dimensional differential equation under noise perturbations are examined. The dynamic structures of some obtained solutions are revealed via some 2D and 3D graphs. The results show that the extended complex method is an efficient and straightforward approach to solving diverse differential equations in mathematical physics.<\/jats:p>","DOI":"10.3390\/axioms14050334","type":"journal-article","created":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T09:39:47Z","timestamp":1745833187000},"page":"334","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Closed-Form Meromorphic Solutions of High-Order and High-Dimensional Differential Equations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7416-2593","authenticated-orcid":false,"given":"Hongqiang","family":"Tu","sequence":"first","affiliation":[{"name":"School of Mathematics, Guangdong University of Education, Guangzhou 510800, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6651-1714","authenticated-orcid":false,"given":"Yongyi","family":"Gu","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"115351","DOI":"10.1016\/j.chaos.2024.115351","article-title":"Soliton, breather, lump, interaction solutions and chaotic behavior for the (2+1)-dimensional KPSKR equation","volume":"187","author":"Gu","year":"2024","journal-title":"Chaos Soliton. 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