For over a hundred years, the theory of water waves has been a source of intriguing and often difficult mathematical problems. Virtually every classical mathematical technique appears somewhere within its confines. Beginning with the introduction of the appropriate equations of fluid mechanics, the opening chapters of this text consider the classical problems in linear and nonlinear water-wave theory. This sets the stage for a study of more modern aspects, problems that give rise to soliton-type equations. The book closes with an introduction to the effects of viscosity. All the mathematical developments are presented in the most straightforward manner, with worked examples and simple cases carefully explained. Exercises, further reading, and historical notes on some of the important characters in the field round off the book and make this an ideal text for a beginning graduate course on water waves.
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"...reasonably priced, and it is one of the best books available on the subject. With suitable supplements by the instructor, it could serve as a very readable text for an interesting course on the modern theory of water waves." Mathematical Reviews
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The theory of water waves has been a source of intriguing and oftendifficult mathematical problems for at least 150 years. This text briefly discusses fluid mechanics. It then considers the classical problems in linear and non-linear water-wave theory, as well as more modern aspects -- problems that give rise to soliton-type equations. Lastly it examines the effects of viscosity. All the mathematical developments are presented in a straightforward manner. Exercises, further reading, and historical notes make this an ideal text for graduate students.
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This review is from: A Modern Introduction to the Mathematical Theory of Water Waves (Cambridge Texts in Applied Mathematics) (Paperback)
This book is suitable for understanding the fundamental theory of shallow water waves. The presentation is easy to follow. It helps me with my research in fluid dynamics since it provides interesting topics in shallow water waves. I like this book.
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Inside This Book
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First Sentence:
"Before we commence our presentation of the theory of water waves, we require a firm and precise base from which to start." Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
two influence points, underlying shear flow, two surface boundary conditions, undular bore, completely integrable equations, arbitrary shear, bilinear method, nonlinear dispersive waves, bottom boundary condition, solitary wave, uniform validity, stationary water, soliton theory, decay conditions, conserved densities, nonlinear wave propagation, conserved density, hydraulic jump, slow modulation, group speed, shallow water equations, crossing waves, viscous contribution, nondimensional variables, gravity waves Key Phrases - Capitalized Phrases (CAPs): (learn more)
Korteweg-de Vries, Newton's Second Law, Scott Russell New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
"Before we commence our presentation of the theory of water waves, we require a firm and precise base from which to start." Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
two influence points, underlying shear flow, two surface boundary conditions, undular bore, completely integrable equations, arbitrary shear, bilinear method, nonlinear dispersive waves, bottom boundary condition, solitary wave, uniform validity, stationary water, soliton theory, decay conditions, conserved densities, nonlinear wave propagation, conserved density, hydraulic jump, slow modulation, group speed, shallow water equations, crossing waves, viscous contribution, nondimensional variables, gravity waves Key Phrases - Capitalized Phrases (CAPs): (learn more)
Korteweg-de Vries, Newton's Second Law, Scott Russell New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 40
books:
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16
books
cite this book:
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- Perturbation Methods (Cambridge Texts in Applied Mathematics) by E. J. Hinch in Front Matter, and Back Matter
- Differential Equations by HABERMAN in Back Matter
- Perturbation Methods in Fluid Mechanics by Milton D. Van Dyke in Back Matter
- Introduction to Water Waves (Mathematics and Its Applications (Ellis Horwood Ltd)) by G. D. Crapper in Back Matter
- Partial Differential Equations (AMS Chelsea Publishing) by Paul R. Garabedian in Back Matter
See all 40 books this book cites
- An Introduction to Parallel and Vector Scientific Computing (Cambridge Texts in Applied Mathematics) by Ronald W. Shonkwiler in Front Matter
- Nonlinear Wave Processes in Acoustics (Cambridge Texts in Applied Mathematics) by K. Naugolnykh in Front Matter
- Symmetry Methods for Differential Equations: A Beginner's Guide (Cambridge Texts in Applied Mathematics) by Peter E. Hydon in Front Matter
- An Introduction to Magnetohydrodynamics (Cambridge Texts in Applied Mathematics) by P. A. Davidson in Front Matter
- Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition by Lokenath Debnath in Back Matter
See all 16 books citing this book
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