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Seminar Mathematical Physics, AAMP Spring 2005 Assignment 1

Summary: Seminar Mathematical Physics, AAMP Spring 2005
Assignment 1
Sheets 24 March
1 page summary Variational Techniques
Further reading: Applied Analytical Methods, part 2
Title Seminar Mathematical Physics Spring 2005
E. van Groesen, UTwente (groesen@math.utwente.nl)
Assignment 1
Assignment 1 has to be handed in before the 7 April meeting.
The Korteweg- de Vries (KdV) equation describes the surface elevation (x; t) of a layer of water
above an even bottom. In normalised variables, and in a frame moving with the velocity of small,
long waves, the equation is given by
@t + @3
x + @x = 0: (1)
1. Write the equation in the form
@t = @x H ( ) (2)
for a suitable functional H ( ).
2. Specify a class of wave elevations so that for that class @x is a skew-symmetric operator. Argue
that on this class the KdV is a Hamiltonian system with Hamiltonian H. In the following we
will work on this class.


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering