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/