Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis

This overview of some of the main results and recent developments in nonlinear water waves presents fundamental aspects of the field and discusses several important topics of current research interest. It contains selected information about water-wave motion for which advanced mathematical study can be pursued, enabling readers to derive conclusions that explain observed phenomena to the greatest extent possible. The author discusses the underlying physical factors of such waves and explores the physical relevance of the mathematical results that are presented. The material is an expanded version of the author s lectures delivered at the NSF-CBMS Regional Research Conference in the Mathematical Sciences organized by the Mathematics Department of the University of Texas-Pan American in 2010. Audience: The book is intended for mathematicians, physicists, and engineers interested in the interplay between physical concepts and insights and the mathematical ideas and methods that are relevant to specific water-wave phenomena. It is also appropriate as a primary text for graduate-level courses on water waves and a supplementary text for courses on elliptic free boundary problems. Contents: Preface; Chapter 1. Introduction; Chapter 2. Preliminaries; Chapter 3. Wave-current interactions; Chapter 4. Fluid kinematics for wave trains; Chapter 5. Solitary water waves; Chapter 6. Breaking waves; Chapter 7. Modeling tsunamis; Bibliography; Index.