{"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/quasiperiodicity-and-blowup-in-integrable","title":"Quasiperiodicity and blowup in integrable subsystems of nonconservative nonlinear Schrödinger equations","arxiv_id":"2108.00307","date":"2021-07-31","proceeding":null,"authors":["Jonathan Jaquette"],"abstract":"In this paper, we study the dynamics of a class of nonlinear Schr\\\"odinger equation $ i u_t = \\triangle u + u^p $ for $ x \\in \\mathbb{T}^d$. We prove that the PDE is integrable on the space of non-negative Fourier coefficients, in particular that each Fourier coefficient of a solution can be explicitly solved by quadrature. Within this subspace we demonstrate a large class of (quasi)periodic solutions all with the same frequency, as well as solutions which blowup in finite time in the $L^2$ norm.","url_abs":"https://arxiv.org/abs/2108.00307v1","url_pdf":"https://arxiv.org/pdf/2108.00307v1.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":"quasiperiodicity-and-blowup-in-integrable","repo_url":"https://github.com/JCJaquette/Quasiperiodicity-and-blowup-in-integrable-subsystems-of-nonconservative-NLS","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}