| | |
Summary: Title Project Wavepro...les of maximal crest height
E. van Groesen, UTwente (groesen@math.utwente.nl)
MRI -Variational Structures and Methods
Project aim: ...nd pro...les of waves that have maximal crest height, for waves on the whole real line
with ...nite energy, and for periodic waves.
We ...rst use a linear model (quadratic energy and momentum), and then a few aspects of a nonlinear
KdV (Korteweg-de Vries) model.
1 Methodology
We will denote by (x; t) (real valued) wave ...elds depending on the spatial and temporal variables
x; t; when being concerned with the pro...les we will simply write (x). The interest will be in waves
described by a Hamiltonian system with Hamiltonian H and a momentum integral M. For de...niteness
we take as governing evolution equation the Hamiltonian system
@t = @x H ( ) :
Here the Hamiltonian H is a translation invariant integral which is linearly independent from the
momentum functional
M =
Z
1
2
2
|
