A Lagrangian for Water Waves
by
Sasha Balk
JTB 320, 3:20pm Monday, April 7, 1997
Abstract
In 1880 Stokes derived his system of cubic equations for the
coefficients of the Fourier expansion of a steady water wave of finite
amplitude. A century later Longuet-Higgins discovered a system of
quadratic equations for the Stokes coefficients which is equivalent to
the original Stokes system. What is the meaning of this quadratic
system? Is this a shade of integrability?
In this work we have found a Lagrangian for water waves (including
overturning waves). It turns out that the Longuet-Higgins system
directly follows from this Lagrangian.
Besides applications of the Lagrangian to the stability of water waves
and to numerical methods, we will point out the approach to the water
surface singularities and to the investigation of nuclear fusion.
Requests for preprints and reprints to: Alexander Balk, balk@ama.caltech.edu
This source can be found at http://www.math.utah.edu/research/