Asymptotic Perturbation Theory Of Waves
Asymptotic Perturbation Theory Of Waves

Author: Lev Ostrovsky

Publisher: World Scientific

Published: 2014-09-23

Total Pages: 227

ISBN-13: 178326473X

DOWNLOAD EBOOK

This book is an introduction to the perturbation theory for linear and nonlinear waves in dispersive and dissipative media. The main focus is on the direct asymptotic method which is based on the asymptotic expansion of the solution in series of one or more small parameters and demanding finiteness of the perturbations; this results in slow variation of the main-order solution. The method, which does not depend on integrability of basic equations, is applied to quasi-harmonic and non-harmonic periodic waves, as well as to localized waves such as solitons, kinks, and autowaves. The basic theoretical ideas are illustrated by many physical examples throughout the book.

Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics
Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics

Author: John P. Boyd

Publisher: Springer

Published: 2011-09-23

Total Pages: 596

ISBN-13: 9781461558262

DOWNLOAD EBOOK

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.

Introduction to Asymptotic Methods
Introduction to Asymptotic Methods

Author: David Y. Gao

Publisher: CRC Press

Published: 2006-05-03

Total Pages: 270

ISBN-13: 1420011731

DOWNLOAD EBOOK

Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m

Introduction to Perturbation Methods
Introduction to Perturbation Methods

Author: Mark H. Holmes

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 344

ISBN-13: 1461253470

DOWNLOAD EBOOK

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.

Nonlinear Dispersive Waves
Nonlinear Dispersive Waves

Author: Mark J. Ablowitz

Publisher: Cambridge University Press

Published: 2011-09-08

Total Pages: 363

ISBN-13: 1139503480

DOWNLOAD EBOOK

The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.

Advanced Mathematical Methods for Scientists and Engineers I
Advanced Mathematical Methods for Scientists and Engineers I

Author: Carl M. Bender

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 605

ISBN-13: 1475730691

DOWNLOAD EBOOK

A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.

Geometric Perturbation Theory In Physics
Geometric Perturbation Theory In Physics

Author: S M Omohundro

Publisher: World Scientific

Published: 1986-10-31

Total Pages: 588

ISBN-13: 9814603430

DOWNLOAD EBOOK

This book which focusses on mechanics, waves and statistics, describes recent developments in the application of differential geometry, particularly symplectic geometry, to the foundations of broad areas of physics. Throughout the book, intuitive descriptions and diagrams are used to elucidate the mathematical theory. It develops a coordinate-free framework for perturbation theory and uses this to show how underlying symplectic structures arise from physical asymptotes. It describes a remarkable parity between classical mechanics which arises asymptotically from quantum mechanics and classical thermodynamics which arises asymptotically from statistical mechanics. Included here is a section with one hundred unanswered questions for further research.

Slowly Varying Oscillations And Waves: From Basics To Modernity
Slowly Varying Oscillations And Waves: From Basics To Modernity

Author: Lev Ostrovsky

Publisher: World Scientific

Published: 2022-02-23

Total Pages: 372

ISBN-13: 9811247501

DOWNLOAD EBOOK

The beauty of the theoretical science is that quite different physical, biological, etc. phenomena can often be described as similar mathematical objects, by similar differential (or other) equations. In the 20th century, the notion of 'theory of oscillations' and later 'theory of waves' as unifying concepts, meaning the application of similar methods and equations to quite different physical problems, came into being. In the variety of applications (quite possibly in most of them), the oscillatory process is characterized by a slow (as compared with the characteristic period) variation of its parameters, such as the amplitude and frequency. The same is true for the wave processes.This book describes a variety of problems associated with oscillations and waves with slowly varying parameters. Among them the nonlinear and parametric resonances, self-synchronization, attenuated and amplified solitons, self-focusing and self-modulation, and reaction-diffusion systems. For oscillators, the physical examples include the van der Pol oscillator and a pendulum, models of a laser. For waves, examples are taken from oceanography, nonlinear optics, acoustics, and biophysics. The last chapter of the book describes more formal asymptotic perturbation schemes for the classes of oscillators and waves considered in all preceding chapters.

Singular Limits of Dispersive Waves
Singular Limits of Dispersive Waves

Author: N.M. Ercolani

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 373

ISBN-13: 1461524741

DOWNLOAD EBOOK

Proceedings of a NATO ARW and of a Chaos, Order, and Patterns Panel sponsored workshop held in Lyons, France, July 8-12, 1991