Numerical study of the semiclassical limit of the Davey–Stewartson II equations

@article{Klein2014NumericalSO,
  title={Numerical study of the semiclassical limit of the Davey–Stewartson II equations},
  author={Christian Klein and K. Roidot},
  journal={Nonlinearity},
  year={2014},
  volume={27},
  pages={2177 - 2214}
}
We present the first detailed numerical study of the semiclassical limit of the Davey–Stewartson II equations both for the focusing and the defocusing variant. We concentrate on rapidly decreasing initial data with a single hump. The formal limit of these equations for vanishing semiclassical parameter ϵ, the semiclassical equations, is numerically integrated up to the formation of a shock. The use of parallelized algorithms allows one to determine the critical time tc and the critical solution… 

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