{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/time-dependent-solutions-to-the-2d-kuramoto","title":"Time-Dependent Solutions to the 2D Kuramoto-Sivashinsky Equation via Pseudospectral Method on a Rectangular Domain","arxiv_id":"2312.15559","date":"2023-12-24","proceeding":null,"authors":["Jovan Žigić"],"abstract":"This report provides an investigation into solving the Kuramoto-Sivashinsky equation in two spatial dimensions (2DKS) using a pseudo-spectral method on various rectangular periodic domains. The Kuramoto-Sivashinsky equation is a fluid dynamics model that exhibits dynamical features that are highly dependent on the length of the periodic domain. The goals of this report are to describe the mathematical problem; explain the details of the chosen numerical method; inspect solutions and dynamical features for varying grid sizes, step sizes, and domains; and summarize the findings.","url_abs":"https://arxiv.org/abs/2312.15559v2","url_pdf":"https://arxiv.org/pdf/2312.15559v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"time-dependent-solutions-to-the-2d-kuramoto","repo_url":"https://github.com/zigicjovan/2dks_solver","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}