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Tsunamis and hurricanes have had a devastating impact on the population living near the coast during the year 2005. The calculation of the power and intensity of tsunamis and hurricanes are of great importance not only for engineers and meteorologists but also for governments and insurance companies. This book presents new research on the mathematical description of tsunamis and hurricanes. A combination of old and new approaches allows to derive a nonlinear partial differential equation of fifth order describing the steepening up and the propagation of tsunamis. The description includes dissipative terms and does not contain singularities or two valued functions. The equivalence principle of solutions of nonlinear large gas dynamics waves and of solutions of water wave equations will be used. An extension of the continuity equation by a source term due to evaporation rates of salt seawater will help to understand hurricanes. Detailed formula, tables and results of the calculations are given.