Water Waves: The Mathematical Theory With Applications (Classic Reprint)

Science & Math

J. J. Stoker

Physics

Forgotten Books

Excerpt from Water Waves: The Mathematical Theory With Applications The subject of surface gravity waves has great variety whether regarded from the point of View of the types of physical problem which occur, or from the point of View of the mathematical ideas and methods needed to attack them. The physical problems range from discussion of wave motion over sloping beaches to flood waves in rivers, the motion of ships in a sea-way, free oscillations of enclosed bodies of water such as lakes and harbors, and the propagation of frontal discontinuities in the atmosphere, to mention just a few. The mathematical tools employed comprise just about the whole of the tools developed in the classical linear mathematical physics concerned with partial differential equations, as well as a good part of what has been learned about the nonlinear problems of mathe matical physics. Thus potential theory and the theory of the linear wave equation, together with such tools as conformal mapping and complex variable methods in general, the Laplace and Fourier transform techniques, methods employing a Green's function, integral equations, etc. Are used. The nonlinear problems are of both elliptic and hyperbolic type. In spite of the diversity of the material, the book, is not a collection of disconnected topics, written for specialists, and lacking unity and coherence. Instead, considerable pains have been taken to supply the fundamental background in hydrodynamics and also in some of the mathematics needed and to plan the book in order that it should be as much as possible a self - contained and readable whole. Though the contents of the book are outlined in detail below, it has some point to indicate briefly here its general plan. There are four main parts of the book. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Presents underlying principles and theories using an easily understood approach. Focuses specifically on those features of the problems in which nonlinearity results in a variety of distinctive new phenomena that can be treated by techniques both interesting and instructive in themselves and which do not require the use of sophisticated mathematics. Recent work discussed includes the endeavors of Levinson and Smith on the existence and uniqueness of the periodic solution in a general case of the self-excited type, Haag and Dorodnitsyn on asymptotic developments and quantities associated with relaxation oscillations. Along with 5 appendices containing rigorous existence and uniqueness proofs, readers are both implicitly and explicitly supplied with hints regarding new problems to be tackled plus numerous ideas and techniques that can be used to solve them.

Nonlinear Vibrations In Mechanical and Ele

Engineering & Transportation

Engineering

Interscience Publishers, Inc.

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