This monograph provides a comprehensive and self-contained study on
the theory of water waves equations, a research area that has been
very active in recent years. The vast literature devoted to the
study of water waves offers numerous asymptotic models. Which model
provides the best description of waves such as tsunamis or tidal
waves? How can water waves equations be transformed into simpler
asymptotic models for applications in, for example, coastal
oceanography? This book proposes a simple and robust framework for
studying these questions. The book should be of interest to
graduate students and researchers looking for an introduction to
water waves equations or for simple asymptotic models to describe
the propagation of waves. Researchers working on the mathematical
analysis of nonlinear dispersive equations may also find
inspiration in the many (and sometimes new) models derived here, as
well as precise information on their physical relevance.
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