[{"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-06-29T09:59:46Z","page":"191-221","citation":{"ieee":"R. Killip, S. Kwon, S. Shao, and M. Vişan, “On the mass-critical generalized KdV equation,” <i>Discrete and Continuous Dynamical Systems</i>, vol. 32, no. 1. American Institute of Mathematical Sciences, pp. 191–221, 2012.","short":"R. Killip, S. Kwon, S. Shao, M. Vişan, Discrete and Continuous Dynamical Systems 32 (2012) 191–221.","ista":"Killip R, Kwon S, Shao S, Vişan M. 2012. On the mass-critical generalized KdV equation. Discrete and Continuous Dynamical Systems. 32(1), 191–221.","apa":"Killip, R., Kwon, S., Shao, S., &#38; Vişan, M. (2012). On the mass-critical generalized KdV equation. <i>Discrete and Continuous Dynamical Systems</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/dcds.2012.32.191\">https://doi.org/10.3934/dcds.2012.32.191</a>","mla":"Killip, Rowan, et al. “On the Mass-Critical Generalized KdV Equation.” <i>Discrete and Continuous Dynamical Systems</i>, vol. 32, no. 1, American Institute of Mathematical Sciences, 2012, pp. 191–221, doi:<a href=\"https://doi.org/10.3934/dcds.2012.32.191\">10.3934/dcds.2012.32.191</a>.","chicago":"Killip, Rowan, Soonsik Kwon, Shuanglin Shao, and Monica Vişan. “On the Mass-Critical Generalized KdV Equation.” <i>Discrete and Continuous Dynamical Systems</i>. American Institute of Mathematical Sciences, 2012. <a href=\"https://doi.org/10.3934/dcds.2012.32.191\">https://doi.org/10.3934/dcds.2012.32.191</a>.","ama":"Killip R, Kwon S, Shao S, Vişan M. On the mass-critical generalized KdV equation. <i>Discrete and Continuous Dynamical Systems</i>. 2012;32(1):191-221. doi:<a href=\"https://doi.org/10.3934/dcds.2012.32.191\">10.3934/dcds.2012.32.191</a>"},"abstract":[{"lang":"eng","text":"We consider the mass-critical generalized Korteweg{de Vries equation (∂t + ∂xxx)u = ±∂ x(u 5) for real-valued functions u(t; x). We prove that if the global well-posedness and scattering conjecture for this equation failed, then, conditional on a positive answer to the global well-posedness and scattering conjecture for the masscritical nonlinear Schrffodinger equation (-i∂ t + ∂xx)u = ±(|u| 4u), there exists a minimal-mass blowup solution to the mass-critical generalized KdV equation which is almost periodic modulo the symmetries of the equation. Moreover, we can guarantee that this minimal-mass blowup solution is either a self-similar solution, a soliton-like solution, or a double high-to-low frequency cascade solution."}],"_id":"22056","doi":"10.3934/dcds.2012.32.191","article_processing_charge":"No","oa_version":"Preprint","OA_type":"green","type":"journal_article","publication":"Discrete and Continuous Dynamical Systems","volume":32,"day":"01","month":"01","language":[{"iso":"eng"}],"extern":"1","publication_status":"published","external_id":{"arxiv":["0907.5412"]},"arxiv":1,"status":"public","author":[{"first_name":"Rowan","last_name":"Killip","full_name":"Killip, Rowan"},{"last_name":"Kwon","full_name":"Kwon, Soonsik","first_name":"Soonsik"},{"first_name":"Shuanglin","last_name":"Shao","full_name":"Shao, Shuanglin"},{"first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan","full_name":"Visan, Monica"}],"OA_place":"repository","publisher":"American Institute of Mathematical Sciences","das_tickbox":"1","intvolume":"        32","year":"2012","publication_identifier":{"issn":["1078-0947"],"eissn":["1553-5231"]},"date_created":"2026-06-19T07:57:09Z","quality_controlled":"1","date_published":"2012-01-01T00:00:00Z","article_type":"original","scopus_import":"1","mathsc":["35Q53"],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.0907.5412"}],"issue":"1","title":"On the mass-critical generalized KdV equation"}]