Author : P. A. Martin
Publisher : Cambridge University Press
Page : 262 pages
File Size : 47,2 MB
Release : 1992-05-29
Category : Mathematics
ISBN : 9780521414142
This volume contains papers by distinguished researchers in fluid mechanics and asymptotics. The papers collected here outline the development of these topics.
Author : David Lannes
Publisher : American Mathematical Soc.
Page : 347 pages
File Size : 49,8 MB
Release : 2013-05-08
Category : Mathematics
ISBN : 0821894706
This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models.
Author : Fritz Ursell
Publisher : World Scientific
Page : 452 pages
File Size : 20,68 MB
Release : 1994
Category : Differential equations, Linear
ISBN : 9789810219505
Author : John P. Boyd
Publisher : Springer
Page : 596 pages
File Size : 35,4 MB
Release : 2011-09-23
Category : Mathematics
ISBN : 9781461558262
This is the first thorough examination of weakly nonlocal solitary waves, which are just as important in applications as their classical counterparts. The book describes a class of waves that radiate away from the core of the disturbance but are nevertheless very long-lived nonlinear disturbances.
Author : M.V. Fedoryuk
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 24,74 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642584233
In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution.
Author : Maarten W. Dingemans
Publisher : World Scientific
Page : 508 pages
File Size : 11,29 MB
Release : 2000
Category : Technology & Engineering
ISBN : 9789810239947
Author : Maarten W Dingemans
Publisher : World Scientific
Page : 1015 pages
File Size : 22,10 MB
Release : 1997-01-07
Category : Technology & Engineering
ISBN : 9814506583
The primary objective of this book is to provide a review of techniques available for the problems of wave propagation in regions with uneven beds as they are encountered in coastal areas. The view taken is that the techniques should be useful for application in advisory practice. However, effort is put into a precise definition of the underlying physical principles, so that the validity of the methods used can be evaluated. Both linear and nonlinear wave propagation techniques are discussed. Because of its length, the book comes in two parts: Part 1 covers primarily linear wave propagation, and Part 2 covers nonlinear wave propagation.
Author : Peter David Miller
Publisher : American Mathematical Soc.
Page : 488 pages
File Size : 26,84 MB
Release : 2006
Category : Mathematics
ISBN : 0821840789
This book is a survey of asymptotic methods set in the current applied research context of wave propagation. It stresses rigorous analysis in addition to formal manipulations. Asymptotic expansions developed in the text are justified rigorously, and students are shown how to obtain solid error estimates for asymptotic formulae. The book relates examples and exercises to subjects of current research interest, such as the problem of locating the zeros of Taylor polynomials of entirenonvanishing functions and the problem of counting integer lattice points in subsets of the plane with various geometrical properties of the boundary. The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and appliedmathematics as well as science and engineering. The basic prerequisite is a background in differential equations, linear algebra, advanced calculus, and complex variables at the level of introductory undergraduate courses on these subjects. The book is ideally suited to the needs of a graduate student who, on the one hand, wants to learn basic applied mathematics, and on the other, wants to understand what is needed to make the various arguments rigorous. Down here in the Village, this is knownas the Courant point of view!! --Percy Deift, Courant Institute, New York Peter D. Miller is an associate professor of mathematics at the University of Michigan at Ann Arbor. He earned a Ph.D. in Applied Mathematics from the University of Arizona and has held positions at the Australian NationalUniversity (Canberra) and Monash University (Melbourne). His current research interests lie in singular limits for integrable systems.
Author : Alexander A. Kaufman
Publisher : Gulf Professional Publishing
Page : 640 pages
File Size : 32,93 MB
Release : 2000
Category : Acoustic surface waves
ISBN : 9780444506429
This book is a continuation of 'Acoustic and Elastic Wave Fields in Geophysics, Part I' published in 2000. The second volume is dedicated to propagation of linear plane, spherical and cylindrical acoustic waves in different media. Chapter 1 is devoted to principles of geometric acoustic in plane wave approximation. The eikonal and transport equations are derived. Ray tracing and wavefront construction techniques are explained. Chapter 2 deals with dynamic properties of wave fields. The behavior of pressure and displacements amplitudes in zero approximation is analysed in two ways: using Poynting vector and solving the transport equation. This chapter contains several examples related to shadow zones and caustics. In Chapter 3 using the results of analysis of high-frequency wave kinematics and dynamics some fundamental aspects of Kirchhoff migration are described. Chapters 4 and 5 are devoted to propagation of plane waves in media with flat boundaries in the case of normal and oblique incidence. Special attention is paid to the case when an incident angle exceeds the critical angles. Formation of normal modes in the waveguide is discussed. Chapter 6 deals with a spherical wave reflection and refraction. The steepest descent method is introduced to describe the behavior of reflected, transmitted, head and evanescent waves. In Chapter 7 propagation of stationary and transient waves in a waveguide formed by a flat layer with low velocity are investigated. Normal modes and waves related to the branch points of integrands under consideration are studied. Dispersive properties of normal modes are discussed. Chapter 8 describes wave propagation inside cylinder in acoustic media. Several appendices are added to help the reader understand different aspects of mathematics used in the book.
Author : A.S. Fokas
Publisher : Springer Science & Business Media
Page : 563 pages
File Size : 42,92 MB
Release : 2012-12-06
Category : Science
ISBN : 3642580459
In the last ten to fifteen years there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum gravity (the connection of the KdV with matrix models). This is the first book to present a comprehensive overview of these developments. Numbered among the authors are many of the most prominent researchers in the field.
