|MadSci Network: Physics|
Let me begin by stating that I'm no expert on ocean waves, or any sort of waves, for that matter. However, I think I may be able to point you to some resources which are created by experts.
You ask about "monster waves". I believe you are referring to what are more commonly called "rogue waves:" isolated waves which are very much taller than the ordinary waves in some region. They can rise far above the ocean surface. In 1995, for example, an oil rig in the North Sea was hit by a wave with a height of 26 meters! Obviously, waves of this size are a menace to ships, so mariners as well as scientists would like to understand their origin; it might help us to avoid them.
You also mention "Schroedinger waves." Erwin Schroedinger (his name is more properly spelled with an umlaut over the o, instead of a following "e", but I prefer to use plain ASCII here) was an Austrian physicist of the early twentieth century who helped to develop quantum mechanics. He is best known for his approach to describing the behavior of atoms and particles as waves of a particular sort. You can find a good biography with plenty of references to additional information at
How are these two ideas related? Well, I learned that oceanologists (is that the right name for scientists who study waves in the ocean?) have found that rogue waves aren't easily explained by "ordinary" wave behaviors. Under ordinary circumstances, if two waves happen to meet as they pass through a large body of water, they combine in a linear fashion: you can simply add the height of the first to the height of the second to find the height of the combined wave. Rogue waves, however, don't appear to have the properties you would expect -- frequency of appearance, lifetime, height compared to surroundings -- from a simple linear combination of waves from a typical population in the ocean.
Some scientists therefore attempt to apply a more complicated model of wave behavior to these situation. It turns out that one sort of equation studied by Schroedinger -- a non-linear variety of wave equation -- may do a better job of explaining the observed properties of rogue waves. You can read much more about this idea at a very nice web page created by scientists at the University of Bergen in Norway:
Finally, let me mention a recent development in the study of rogue waves: the European Space Agency launched a pair of satellites to monitor the ocean's surface: ERS-1 (launched in 1991) and ERS-2 (launched in 1995) use synthetic aperture radar to measure the height of the surface in a wide swathe beneath their orbital tracks. They can apparently detect waves just a small fraction of a meter in height, so rogue waves stand out clearly: just look at the figure labelled Giant wave detected in ERS-2 imagette data in the ESA's web page
I hope these references will help you to learn more about rogue waves and their connection to Schroedinger's mathematics. As far as I can tell from reading the papers myself, scientists cannot yet predict where and when rogue waves will occur.
Try the links in the MadSci Library for more information on Physics.