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Cambridge Texts in Applied Mathematics #0019: A Modern Introduction to the Mathematical Theory of Water Wavesby R. S. Johnson
Synopses & ReviewsPublisher Comments: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 waterwave theory. This sets the stage for a study of more modern aspects, problems that give rise to solitontype 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.
Synopsis: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 nonlinear waterwave theory, as well as more modern aspects — problems that give rise to solitontype 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.
Synopsis:This text considers classical and modern problems in linear and nonlinear waterwave theory.
Table of Contents1. Mathematical preliminaries; 2. Some classical problems in waterwave theory; 3. Weakly nonlinear dispersive waves; 4. Slow modulation of dispersive waves; 5. Epilogue.
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