Justification of the Nonlinear Schrodinger Equation for the Evolution of Gravity Driven 2D Surface Water Waves in a Canal of Finite Depth

摘要

In 1968 V.E. Zakharov derived the Nonlinear Schrodinger equation for the two-dimensional water wave problem in the absence of surface tension, that is, 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 approximated over a physically relevant timespan by solutions of the Nonlinear Schrodinger equation.