Formation of Three-Dimensional Surface Waves on Deep-Water Using Elliptic Solutions of Nonlinear Schrödinger Equation

@article{Sajjadi2015FormationOT,
  title={Formation of Three-Dimensional Surface Waves on Deep-Water Using Elliptic Solutions of Nonlinear Schr{\"o}dinger Equation},
  author={Shahrdad G. Sajjadi and Stefan C. Mancas and Fr{\'e}d{\'e}rique Drullion},
  journal={Advances and Applications in Fluid Mechanics},
  year={2015},
  volume={18},
  pages={81-112}
}
A review of three-dimensional waves on deep-water is presented. Three forms of three dimensionality, namely oblique, forced and spontaneous type, are identified. An alternative formulation for these three-dimensional waves is given through cubic nonlinear Schr\"odinger equation. The periodic solutions of the cubic nonlinear Schr\"odinger equation are found using Weierstrass elliptic $\wp$ functions. It is shown that the classification of solutions depends on the boundary conditions, wavenumber… 

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