@article{22081,
  abstract     = {We consider the Cauchy problem for a family of semilinear defocusing Schrödinger equations with monomial nonlinearities in one space dimension. We establish global well-posedness and scattering. Our analysis is based on a four-particle interaction Morawetz estimate giving a priori $L_{t,x}^8$ spacetime control on solutions.},
  author       = {Colliander, J. and Holmer, Justin and Visan, Monica and Zhang, Xiaoyi},
  issn         = {1553-5258},
  journal      = {Communications on Pure and Applied Analysis},
  number       = {3},
  pages        = {467--489},
  publisher    = {American Institute of Mathematical Sciences},
  title        = {{Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$}},
  doi          = {10.3934/cpaa.2008.7.467},
  volume       = {7},
  year         = {2008},
}