Cambridge University Press, UK, 2016. – 300 p. – ISBN: 1107565561In the summer of 2014 leading experts in the theory of water waves gathered at the Newton Institute for Mathematical Sciences in Cambridge for four weeks of research interaction. A cross-section of those experts was invited to give introductory-level talks on active topics. This book is a compilation of those talks and illustrates the diversity, intensity, and progress of current research in this area. The key themes that emerge are numerical methods for analysis, stability and simulation of water waves, transform methods, rigorous analysis of model equations, three-dimensionality of water waves, variational principles, shallow water hydrodynamics, the role of deterministic and random bottom topography, and modulation equations. This book is an ideal introduction for PhD students and researchers looking for a research project. It may also be used as a supplementary text for advanced courses in mathematics or fluid dynamics. Contents High-Order Perturbation of Surfaces Short Course: Boundary Value Problems High-Order Perturbation of Surfaces Short Course: Traveling Water Waves High-Order Perturbation of Surfaces Short Course: Analyticity Theory High-Order Perturbation of Surfaces Short Course: Stability of Traveling Water Waves A Novel Non-Local Formulation of Water Waves The Dimension-Breaking Route to Three-Dimensional Solitary Gravity-Capillary Water Waves Validity and Non-Validity of the Nonlinear Schrödinger Equation as a Model for Water Waves Vortex Sheet Formulations and Initial Value Problems: Analysis and Computing Wellposedness and Singularities of the Water Wave Equations Conformal Mapping and Complex Topographies Variational Water Wave Modelling: from Continuum to Experiment Symmetry, Modulation, and Nonlinear Waves
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