Tsunamis and hurricanes are natural catastrophes which can make cons- erable material damage and personal harm to humans. Any possibility to describe these phenomena and to ?nd methods of predictability of any kind seem therefore to be of interest not only for meteorologists, but also for governments, evacuation plans or the insurance industry etc. There may now exist a chance to satisfy these needs, if a tsunami wave equation could be found and solved. Seismic waves in the Earth s crust propagate faster (4 6 km/sec) than tsunamis (100 900 km/h). This speed di'erence allows an early warning time of up to a few hours, depending on the location of the earthquake or underwater explosion. If a tsunami wave equation and its solutions were known, even a guess of the tsunami crest height might be possible and useful. In this book a mathematical approach to tsunami wave equations is p- sented. To the author s knowledge some of the tools and computer codes presentedherehavenever beenappliedontsunamisandhurricanes.

Someof the calculations in this book are based on thePreiswerk-Landau equ- alence principle between gasdynamics and hydrodynamics as well on the Bechert-Marx linearization method using the mass variable transfor- tion. Other tools used here are similarity transformations and the program packet Mathematica by Wolfram. Although knowledge of these codes is not necessary for the use of this book, it may however help to understand some calculations and the reader may acquire some knowledge of this p- gram.".