article published yes Rowan Killip author Soonsik Kwon author Shuanglin Shao author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca 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. American Institute of Mathematical Sciences2012 eng 1078-0947 1553-5231 0907.541210.3934/dcds.2012.32.191 321191-221 yes 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> 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>. 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>. 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> 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. R. Killip, S. Kwon, S. Shao, M. Vişan, Discrete and Continuous Dynamical Systems 32 (2012) 191–221. 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. 220562026-06-19T07:57:09Z2026-06-29T09:59:46Z