@article{22056,
  abstract     = {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.},
  author       = {Killip, Rowan and Kwon, Soonsik and Shao, Shuanglin and Visan, Monica},
  issn         = {1553-5231},
  journal      = {Discrete and Continuous Dynamical Systems},
  number       = {1},
  pages        = {191--221},
  publisher    = {American Institute of Mathematical Sciences},
  title        = {{On the mass-critical generalized KdV equation}},
  doi          = {10.3934/dcds.2012.32.191},
  volume       = {32},
  year         = {2012},
}