The Solitary Wave and Periodic Waves in Shallow Water

The Solitary Wave and Periodic Waves in Shallow Water
Author: Joseph B Keller
Publisher: Legare Street Press
Total Pages: 0
Release: 2023-07-18
Genre:
ISBN: 9781019586051

This book is a detailed study of solitary waves and periodic waves in shallow water. The author, Joseph B. Keller, is a renowned mathematician with extensive expertise in applied mathematics. In this book, he provides a comprehensive analysis of the physical phenomena associated with the propagation of waves in shallow water. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Mathematics of Complexity and Dynamical Systems

Mathematics of Complexity and Dynamical Systems
Author: Robert A. Meyers
Publisher: Springer Science & Business Media
Total Pages: 1885
Release: 2011-10-05
Genre: Mathematics
ISBN: 1461418054

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Solitary Waves in Fluids

Solitary Waves in Fluids
Author: R. Grimshaw
Publisher: WIT Press
Total Pages: 209
Release: 2007
Genre: Science
ISBN: 1845641574

Edited by R.H.J. Grimshaw, this book covers the topic of solitary waves in fluids.

Water Wave Mechanics For Engineers And Scientists

Water Wave Mechanics For Engineers And Scientists
Author: Robert G Dean
Publisher: World Scientific Publishing Company
Total Pages: 369
Release: 1991-01-23
Genre: Technology & Engineering
ISBN: 9814365696

This book is intended as an introduction to classical water wave theory for the college senior or first year graduate student. The material is self-contained; almost all mathematical and engineering concepts are presented or derived in the text, thus making the book accessible to practicing engineers as well.The book commences with a review of fluid mechanics and basic vector concepts. The formulation and solution of the governing boundary value problem for small amplitude waves are developed and the kinematic and pressure fields for short and long waves are explored. The transformation of waves due to variations in depth and their interactions with structures are derived. Wavemaker theories and the statistics of ocean waves are reviewed. The application of the water particle motions and pressure fields are applied to the calculation of wave forces on small and large objects. Extension of the linear theory results to several nonlinear wave properties is presented. Each chapter concludes with a set of homework problems exercising and sometimes extending the material presented in the chapter. An appendix provides a description of nine experiments which can be performed, with little additional equipment, in most wave tank facilities.

Partial Differential Equations and Solitary Waves Theory

Partial Differential Equations and Solitary Waves Theory
Author: Abdul-Majid Wazwaz
Publisher: Springer Science & Business Media
Total Pages: 700
Release: 2010-05-28
Genre: Mathematics
ISBN: 364200251X

"Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineering, and other related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University, Chicago, Illinois, USA.

Encyclopedia of Complexity and Systems Science

Encyclopedia of Complexity and Systems Science
Author:
Publisher: Springer
Total Pages: 10398
Release: 2009-06-26
Genre: Science
ISBN: 9780387758886

This encyclopedia provides an authoritative single source for understanding and applying the concepts of complexity theory together with the tools and measures for analyzing complex systems in all fields of science and engineering. It links fundamental concepts of mathematics and computational sciences to applications in the physical sciences, engineering, biomedicine, economics and the social sciences.

Applications of Symmetry Methods to Partial Differential Equations

Applications of Symmetry Methods to Partial Differential Equations
Author: George W. Bluman
Publisher: Springer Science & Business Media
Total Pages: 415
Release: 2009-10-30
Genre: Mathematics
ISBN: 0387680284

This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Bäcklund symmetries, contact transformations, adjoint symmetries, Nöther's Theorem, mappings with some modification, potential symmetries, nonlocal symmetries, nonlocal mappings, and non-classical method. Of use to graduate students and researchers in mathematics and physics.

Water Waves: The Mathematical Theory with Applications

Water Waves: The Mathematical Theory with Applications
Author: James Johnston Stoker
Publisher: Courier Dover Publications
Total Pages: 593
Release: 2019-04-17
Genre: Science
ISBN: 0486839923

First published in 1957, this is a classic monograph in the area of applied mathematics. It offers a connected account of the mathematical theory of wave motion in a liquid with a free surface and subjected to gravitational and other forces, together with applications to a wide variety of concrete physical problems. A never-surpassed text, it remains of permanent value to a wide range of scientists and engineers concerned with problems in fluid mechanics. The four-part treatment begins with a presentation of the derivation of the basic hydrodynamic theory for non-viscous incompressible fluids and a description of the two principal approximate theories that form the basis for the rest of the book. The second section centers on the approximate theory that results from small-amplitude wave motions. A consideration of problems involving waves in shallow water follows, and the text concludes with a selection of problems solved in terms of the exact theory. Despite the diversity of its topics, this text offers a unified, readable, and largely self-contained treatment.