Having seen how easy it is to solve wave equations using
Fourier theory, here is an enigma for partial differential
equations which is not yet solved. It it the question about
Monster waves. Discovered in 1995, one estimates that at every
moment, about 10-20 monster waves exist on the ocean. These are
waves reaching up to 30 meters (90 feet) Whats the problem?
The problem is that theory does not give an explanation for
their existence. Only up to 15 meter high waves are expected.
Monster waves are dangerous for ships. They are rare, but there
are indications that some ship accidents are due to monster waves.
Theoretical work is not only scientifically important. Understanding
the mechanisms for monster waves could help to predict them or
at least to estimate the risks, which is important for insurance
companies for example.
A swiss TV coverage
has recently dealt with this: