Lectures on the theory of water waves [E-Book] / edited by Thomas J. Bridges (University of Surrey), Mark D. Groves (Universität des Saarlandes, Saarbrücken, Germany) and David P. Nicholls (University of Illinois, Chicago).
Bridges, Thomas J., (editor)
Groves, Mark D., (editor) / Nicholls, David P., (editor)
Cambridge : Cambridge University Press, 2016
1 online resource (xiv, 283 pages)
englisch
9781316411155
9781107565562
London Mathematical Society lecture note series ; 426
Full Text
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505 0 |a High-Order Perturbation of Surfaces (HOPS) Short Course--boundary value problems / David P. Nicholls -- HOPS Short Course--traveling water waves / Benjamin F. Akers -- High-Order Perturbation of Surfaces (HOPS) Short Course--analyticity theory / David P. Nicholls -- HOPS Short Course--stability of travelling water waves / Benjamin F. Akers -- A novel non-local formulation of water waves / Athanassios S. Fokas and Konstantinos Kalimeris -- The dimension-breaking route to three-dimensional solitary gravity-capillary water waves / Mark D. Groves -- Validity and non-validity of the nonlinear Schrödinger equation as a model for water waves / Guido Schneider -- Vortex sheet formulations and initial value problems: analysis and computing / David M. Ambrose -- Wellposedness and singularities of the water wave equations / Sijue Wu -- Conformal mapping and complex topographies / André Nachbin -- Variational water wave modelling: from continuum to experiment / Onno Bokhove and Anna Kalogirou -- Symmetry, modulation and nonlinear waves / Thomas J. Bridges. 
520 |a 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. 
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