Archive for Rational Mechanics and Analysis

, Volume 220, Issue 2, pp 543–602 | Cite as

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

  • Wolf-Patrick Düll
  • Guido Schneider
  • C. Eugene Wayne
Article
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Abstract

In 1968 V.E. Zakharov derived the Nonlinear Schrödinger 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 Schrödinger equation.

Keywords

Water Wave Lagrangian Formulation Local Existence Fourier Space Bilinear Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Wolf-Patrick Düll
    • 1
  • Guido Schneider
    • 1
  • C. Eugene Wayne
    • 2
  1. 1.Institut für Analysis, Dynamik und ModellierungUniversität StuttgartStuttgartGermany
  2. 2.Department of Mathematics and Statistics and Center for BiodynamicsBoston UniversityBostonUSA

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