Madelung, Gross-Pitaevskii and Korteweg

@article{Carles2012MadelungGA,
  title={Madelung, Gross-Pitaevskii and Korteweg},
  author={R{\'e}mi Carles and Rapha{\"e}l Danchin and Jean-Claude Saut},
  journal={Nonlinearity},
  year={2012},
  volume={25},
  pages={2843-2873}
}
This paper surveys various aspects of the hydrodynamic formulation of the nonlinear Schrodinger equation obtained via the Madelung transform in connection to models of quantum hydrodynamics and to compressible fluids of the Korteweg type. 
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