TY - GEN A1 - Bestehorn, Michael A1 - Tyvand, Peder A. A1 - Michelitsch, Thomas M. T1 - Dimension-Reduced Model for Deep-Water Waves T2 - Journal of Applied Mathematics and Physics N2 - Starting from the 2D Euler equations for an incompressible potential flow, a dimension-reduced model describing deep-water surface waves is derived. Similar to the Shallow-Water case, the z-dependence of the dependent variables is found explicitly from the Laplace equation and a set of two one- dimensional equations in x for the surface velocity and the surface elevation remains. The model is nonlocal and can be formulated in conservative form, describing waves over an infinitely deep layer. Finally, numerical solutions are presented for several initial conditions. The side-band instability of Stokes waves and stable envelope solitons are obtained in agreement with other work. The conservation of the total energy is checked. KW - Hydrodynamics KW - Ocean Waves KW - DeepWater Waves KW - Numerical Solutions KW - Fractal Derivatives Y1 - 2019 UR - https://www.scirp.org/journal/paperabs.aspx?paperid=89888 U6 - https://doi.org/10.4236/jamp.2019.71007 SN - 2327-4379 SN - 2327-4352 VL - 7 IS - 1 SP - 72 EP - 92 ER -