@article{22069,
  abstract     = {For slowly-varying initial data, solutions to the Ablowitz–Ladik system have been proven to converge to solutions of the cubic Schrödinger equation. In this paper we show that in the continuum limit, solutions to the Ablowitz–Ladik system with H^1 initial data may also converge to solutions of the modified Korteweg–de Vries equation. To exhibit this new limiting behavior, it suffices that the initial data is supported near the inflection points of the dispersion relation associated with the Ablowitz–Ladik system.

Our arguments employ harmonic analysis tools, Strichartz estimates, and the conservation of mass and energy. Correspondingly, they are applicable beyond the completely integrable models of greatest interest to us.},
  author       = {Killip, Rowan and Ouyang, Zhimeng and Visan, Monica and Wu, Lei},
  issn         = {1553-5231},
  journal      = {Discrete and Continuous Dynamical Systems},
  number       = {3},
  pages        = {821--846},
  publisher    = {American Institute of Mathematical Sciences},
  title        = {{The modified Korteweg–de Vries limit of the Ablowitz–Ladik system}},
  doi          = {10.3934/dcds.2024114},
  volume       = {45},
  year         = {2025},
}

@article{17231,
  abstract     = {In the class of projective billiards, which contains the usual billiards, we exhibit counter-examples to Ivrii's conjecture, which states that in any planar billiard with smooth boundary the set of periodic orbits has zero measure. The counter-examples are polygons admitting a 2-parameters family of n-periodic orbits, with n being either 3 or any even integer greater than 4.},
  author       = {Fiorebe, Corentin},
  issn         = {1553-5231},
  journal      = {Discrete and Continuous Dynamical Systems- Series A},
  number       = {11},
  pages        = {3287--3301},
  publisher    = {AIMS},
  title        = {{Examples of projective billiards with open sets of periodic orbits}},
  doi          = {10.3934/dcds.2024059},
  volume       = {44},
  year         = {2024},
}

@article{22030,
  abstract     = {We consider the mass-subcritical NLS in dimensions d>=3 with radial initial data. In the defocusing case, we prove that any solution that remains bounded in the critical Sobolev space throughout its lifespan must be global and scatter. In the focusing case, we prove the existence of a threshold solution that has a compact flow.},
  author       = {Killip, Rowan and Masaki, Satoshi and Murphy, Jason and Visan, Monica},
  issn         = {1553-5231},
  journal      = {Discrete and Continuous Dynamical Systems},
  number       = {1},
  pages        = {553--583},
  publisher    = {American Institute of Mathematical Sciences},
  title        = {{The radial mass-subcritical NLS in negative order Sobolev spaces}},
  doi          = {10.3934/dcds.2019023},
  volume       = {39},
  year         = {2019},
}

@article{22033,
  abstract     = {We consider the defocusing energy-critical nonlinear Schrödinger
equation with inverse-square potential iut = −∆u + a|x|^−2u + |u|^4u in three
space dimensions. We prove global well-posedness and scattering for a >− 1/4 + 1/25. We also carry out the variational analysis needed to treat the focusing case.},
  author       = {Killip, Rowan and Miao, Changxing and Visan, Monica and Zhang, Junyong and Zheng, Jiqiang},
  issn         = {1553-5231},
  journal      = {Discrete and Continuous Dynamical Systems},
  number       = {7},
  pages        = {3831--3866},
  publisher    = {American Institute of Mathematical Sciences},
  title        = {{The energy-critical NLS with inverse-square potential}},
  doi          = {10.3934/dcds.2017162},
  volume       = {37},
  year         = {2017},
}

@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},
}