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Formation Of Three-Dimensional Surface Waves On Deep-Water Using Elliptic Solutions Of Nonlinear Schrödinger Equation, Shahrdad G. Sajjadi, S.C. Mancas, Frederique Drullion

Publications

A review of three-dimensional waves on deep-water is presented. Three forms of three-dimensionality, namely oblique, forced and spontaneous types, are identified. An alternative formulation for these three-dimensional waves is given through cubic nonlinear Schrödinger equation. The periodic solutions of the cubic nonlinear Schrödinger equation are found using Weierstrass elliptic ℘ functions. It is shown that the classification of solutions depends on the boundary conditions, wavenumber and frequency. For certain parameters, Weierstrass ℘ functions are reduced to periodic, hyperbolic or Jacobi elliptic functions. It is demonstrated that some of these solutions do not have any physical significance. An analytical solution of …