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THE STUDY OF MAXIMAL SURFACES BY LIE SYMMETRY | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 03 آذر 1403 اصل مقاله (1008.42 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2024.62234.2729 | ||
| نویسندگان | ||
| Akram Mohammadpouri* 1؛ Sedigheh Hasannejad2؛ Ali Haji Badali2 | ||
| 1Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran. | ||
| 2Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran. | ||
| چکیده | ||
| Maximal surfaces, a fascinating class of surfaces in differential geometry, are identified by having a mean curvature equal to zero. This distinctive feature gives rise to a nonlinear second-order partial differential equation. In this current article, we delve into the symmetries that underlie the maximal surface equation. Next, we identify one-dimensional optimal system of subalgebras that span these symmetries. It provides a powerful tool to analyze and manipulate the equation, making it easier to study. Finally, since we aim to not only explore the underlying symmetries of the maximal surface equation, we demonstrate how these symmetries can be harnessed to uncover and classify a wide range of maximal surfaces by using reduction methods. | ||
| کلیدواژه‌ها | ||
| catenoid؛ helicoid؛ maximal surface؛ mean curvature؛ symmetry group | ||
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آمار تعداد مشاهده مقاله: 64 تعداد دریافت فایل اصل مقاله: 80 |
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