Lectures on the Theory of Water Waves London Mathematical Society Lecture Note Series

In 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.

Preface Thomas J. Bridges, Mark D. Groves and David P. Nicholls; 1. High-Order Perturbation of Surfaces (HOPS) Short Course – boundary value problems David P. Nicholls; 2. HOPS Short Course – traveling water waves Benjamin F. Akers; 3. High-Order Perturbation of Surfaces (HOPS) Short Course – analyticity theory David P. Nicholls; 4. HOPS Short Course – stability of travelling water waves Benjamin F. Akers; 5. A novel non-local formulation of water waves Athanassios S. Fokas and Konstantinos Kalimeris; 6. The dimension-breaking route to three-dimensional solitary gravity-capillary water waves Mark D. Groves; 7. Validity and non-validity of the nonlinear Schrödinger equation as a model for water waves Guido Schneider; 8. Vortex sheet formulations and initial value problems: analysis and computing David M. Ambrose; 9. Wellposedness and singularities of the water wave equations Sijue Wu; 10. Conformal mapping and complex topographies André Nachbin; 11. Variational water wave modelling: from continuum to experiment Onno Bokhove and Anna Kalogirou; 12. Symmetry, modulation and nonlinear waves Thomas J. Bridges.

Thomas J. Bridges has been researching water waves for over 25 years, with contributions in the areas of shallow water hydrodynamics, breaking waves, resonances, instabilities, Hamiltonian structures, solitary waves, and sloshing. He is currently Professor of Mathematics at the University of Surrey, has over 130 published papers, and is leader of the EPSRC-supported project on modelling water wave energy converters.
Mark D. Groves has been researching the theory of water waves for over 20 years. He is currently Professor at the University of Saarlandes, Saarbrücken, Germany. His principal contributions have been in the areas of dimension breaking, Hamiltonian structures, spatial dynamics, and the applications of dynamical systems theory and nonlinear functional analysis to the problem of water waves.
David P. Nicholls has studied water waves, electromagnetic and acoustic wave propagation, and high-order spectral methods for the past 20 years. He is currently a Professor of Mathematics, Statistics, and Computer Science at the University of Illinois, Chicago. He has over 60 published papers and has received continuous support from the NSF, DOE, and industry.