{"author":[{"last_name":"Killip","full_name":"Killip, Rowan","first_name":"Rowan"},{"id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan","first_name":"Monica","full_name":"Visan, Monica"},{"last_name":"Zhang","first_name":"Xiaoyi","full_name":"Zhang, Xiaoyi"}],"date_updated":"2026-06-22T12:56:27Z","citation":{"apa":"Killip, R., Vişan, M., &#38; Zhang, X. (2021). Finite-dimensional approximation and non-squeezing for the cubic nonlinear Schrödinger equation on ℝ2. <i>American Journal of Mathematics</i>. Johns Hopkins University Press. <a href=\"https://doi.org/10.1353/ajm.2021.0014\">https://doi.org/10.1353/ajm.2021.0014</a>","short":"R. Killip, M. Vişan, X. Zhang, American Journal of Mathematics 143 (2021) 613–680.","ieee":"R. Killip, M. Vişan, and X. Zhang, “Finite-dimensional approximation and non-squeezing for the cubic nonlinear Schrödinger equation on ℝ2,” <i>American Journal of Mathematics</i>, vol. 143, no. 2. Johns Hopkins University Press, pp. 613–680, 2021.","chicago":"Killip, Rowan, Monica Vişan, and Xiaoyi Zhang. “Finite-Dimensional Approximation and Non-Squeezing for the Cubic Nonlinear Schrödinger Equation on ℝ2.” <i>American Journal of Mathematics</i>. Johns Hopkins University Press, 2021. <a href=\"https://doi.org/10.1353/ajm.2021.0014\">https://doi.org/10.1353/ajm.2021.0014</a>.","ista":"Killip R, Vişan M, Zhang X. 2021. Finite-dimensional approximation and non-squeezing for the cubic nonlinear Schrödinger equation on ℝ2. American Journal of Mathematics. 143(2), 613–680.","mla":"Killip, Rowan, et al. “Finite-Dimensional Approximation and Non-Squeezing for the Cubic Nonlinear Schrödinger Equation on ℝ2.” <i>American Journal of Mathematics</i>, vol. 143, no. 2, Johns Hopkins University Press, 2021, pp. 613–80, doi:<a href=\"https://doi.org/10.1353/ajm.2021.0014\">10.1353/ajm.2021.0014</a>.","ama":"Killip R, Vişan M, Zhang X. Finite-dimensional approximation and non-squeezing for the cubic nonlinear Schrödinger equation on ℝ2. <i>American Journal of Mathematics</i>. 2021;143(2):613-680. doi:<a href=\"https://doi.org/10.1353/ajm.2021.0014\">10.1353/ajm.2021.0014</a>"},"publisher":"Johns Hopkins University Press","quality_controlled":"1","scopus_import":"1","publication":"American Journal of Mathematics","status":"public","OA_type":"green","publication_identifier":{"eissn":["1080-6377"]},"oa":1,"day":"01","doi":"10.1353/ajm.2021.0014","extern":"1","oa_version":"Preprint","publication_status":"published","abstract":[{"text":"We prove that solutions of the cubic nonlinear Schr\\\"odinger equation on $\\Bbb{R}^2$ can be approximated by a finite-dimensional Hamiltonian system, uniformly on bounded sets of initial data. This is despite the wealth of non-compact symmetries: scaling, translation, and Galilei boosts.\r\n\r\nComplementing this approximation result, we show that all solutions of the finite-dimensional Hamiltonian system we use can be approximated by the full PDE.\r\n\r\nA key ingredient in these results is the development of a general methodology for transfering uniform global space-time bounds to suitable Fourier truncations of dispersive PDE models.\r\n\r\nAs an application, we prove symplectic non-squeezing (in the sense of Gromov) for the cubic NLS on $\\Bbb{R}^2$. This is the first symplectic non-squeezing result for a Hamiltonian PDE in infinite volume. It is also the first unconditional symplectic non-squeezing result in a scaling-critical setting.\r\n\r\nFinally, we discuss implications of non-squeezing on the nature of scattering.","lang":"eng"}],"page":"613-680","external_id":{"arxiv":["1606.07738"]},"year":"2021","arxiv":1,"title":"Finite-dimensional approximation and non-squeezing for the cubic nonlinear Schrödinger equation on ℝ2","_id":"22035","date_published":"2021-04-01T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1606.07738","open_access":"1"}],"OA_place":"repository","issue":"2","volume":143,"intvolume":"       143","language":[{"iso":"eng"}],"type":"journal_article","das_tickbox":"1","date_created":"2026-06-19T07:43:41Z","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","month":"04"}