Justification of the Nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth
نویسندگان
چکیده
In 1968 V.E. Zakharov derived the Nonlinear Schrödinger equation for the 2D water wave problem in the absence of surface tension, i.e., for the evolution of gravity driven surface water waves, in order to describe slow temporal and spatial modulations of a spatially and temporarily oscillating wave packet. In this paper we give a rigorous proof that the wave packets in the two-dimensional water wave problem in a canal of finite depth can be accurately approximated by solutions of the Nonlinear Schrödinger equation.
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Wissenschaftliche Arbeiten
Attractivity of the Ginz-burg-Landau mode distribution for a pattern forming system with marginally stable long modes. Justification of the 2D NLS equation – Quadratic resonances do not matter in case of analytic initial conditions. Justification of the Nonlinear Schrödinger equation for the evolution of gravity driven 2D surface water waves in a canal of finite depth. approximation of time osc...
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