Asymptotic Perturbation Theory Of Waves

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Asymptotic Perturbation Theory Of Waves

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Author : Ostrovsky Lev
language : en
Publisher: World Scientific
Release Date : 2014-09-23

Asymptotic Perturbation Theory Of Waves written by Ostrovsky Lev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-23 with Juvenile Nonfiction categories.

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.

Asymptotic Perturbation Theory Of Waves

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Author : Lev Ostrovsky
language : en
Publisher:
Release Date : 2014-05-26

Asymptotic Perturbation Theory Of Waves written by Lev Ostrovsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-26 with Science categories.

This book gives an introduction to the perturbation theory for nonlinear waves in dispersive and dissipative media. The popular integrable evolution equations are generalized to include effects of dissipation, inhomogeneity, and media rotation, among others. Non-integrable model equations are also considered. A systematic description of the perturbation method based on the Lagrangian approach is developed in application to solitons, kinks, shock waves, and vortices. Moreover, the interaction of solitary waves in terms of interacting classical particles is presented. All of these basic theoretical ideas are illustrated by many practical examples throughout the book.

Perturbation Theories Evolution Equations And Solitons

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Author : Konstantin Gorshkov
language : en
Publisher: Imperial College Press
Release Date : 2014

Perturbation Theories Evolution Equations And Solitons written by Konstantin Gorshkov and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with SCIENCE categories.

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 theore.

Asymptotic Methods In Nonlinear Wave Theory

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Author : Alan Jeffrey
language : en
Publisher: Pitman Advanced Publishing Program
Release Date : 1982

Asymptotic Methods In Nonlinear Wave Theory written by Alan Jeffrey and has been published by Pitman Advanced Publishing Program this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Science categories.

Weakly Nonlocal Solitary Waves And Beyond All Orders Asymptotics

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Author : John P. Boyd
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Weakly Nonlocal Solitary Waves And Beyond All Orders Asymptotics written by John P. Boyd and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Nonlinear Dispersive Waves

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Author : Mark J. Ablowitz
language : en
Publisher:
Release Date : 2014-05-14

Nonlinear Dispersive Waves written by Mark J. Ablowitz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Asymptotic expansions categories.

Enables graduate students and researchers to understand and employ a wide variety of methods in applied mathematics.

Asymptotic Perturbation Methods

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Author : Attilio Maccari
language : en
Publisher: John Wiley & Sons
Release Date : 2023-01-10

Asymptotic Perturbation Methods written by Attilio Maccari and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-10 with Science categories.

Asymptotic Perturbation Methods Cohesive overview of powerful mathematical methods to solve differential equations in physics Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics addresses nonlinearity in various fields of physics from the vantage point of its mathematical description in the form of nonlinear partial differential equations and presents a unified view on nonlinear systems in physics by providing a common framework to obtain approximate solutions to the respective nonlinear partial differential equations based on the asymptotic perturbation method. Aside from its complete coverage of a complicated topic, a noteworthy feature of the book is the emphasis on applications. There are several examples included throughout the text, and, crucially, the scientific background is explained at an elementary level and closely integrated with the mathematical theory to enable seamless reader comprehension. To fully understand the concepts within this book, the prerequisites are multivariable calculus and introductory physics. Written by a highly qualified author with significant accomplishments in the field, Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics covers sample topics such as: Application of the various flavors of the asymptotic perturbation method, such as the Maccari method to the governing equations of nonlinear system Nonlinear oscillators, limit cycles, and their bifurcations, iterated nonlinear maps, continuous systems, and nonlinear partial differential equations (NPDEs) Nonlinear systems, such as the van der Pol oscillator, with advanced coverage of plasma physics, quantum mechanics, elementary particle physics, cosmology, and chaotic systems Infinite-period bifurcation in the nonlinear Schrodinger equation and fractal and chaotic solutions in NPDEs Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics is ideal for an introductory course at the senior or first year graduate level. It is also a highly valuable reference for any professional scientist who does not possess deep knowledge about nonlinear physics.

Introduction To Asymptotic Methods

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Author : David Y. Gao
language : en
Publisher: CRC Press
Release Date : 2006-05-03

Introduction To Asymptotic Methods written by David Y. Gao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-03 with Mathematics categories.

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

Perturbation Theory For The Schr Dinger Operator With A Periodic Potential

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Author : Yulia E. Karpeshina
language : en
Publisher: Springer
Release Date : 2006-11-14

Perturbation Theory For The Schr Dinger Operator With A Periodic Potential written by Yulia E. Karpeshina and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

The book is devoted to perturbation theory for the Schrödinger operator with a periodic potential, describing motion of a particle in bulk matter. The Bloch eigenvalues of the operator are densely situated in a high energy region, so regular perturbation theory is ineffective. The mathematical difficulties have a physical nature - a complicated picture of diffraction inside the crystal. The author develops a new mathematical approach to this problem. It provides mathematical physicists with important results for this operator and a new technique that can be effective for other problems. The semiperiodic Schrödinger operator, describing a crystal with a surface, is studied. Solid-body theory specialists can find asymptotic formulae, which are necessary for calculating many physical values.

Slowly Varying Oscillations And Waves From Basics To Modernity

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Author : Lev Ostrovsky
language : en
Publisher: World Scientific
Release Date : 2022-02-23

Slowly Varying Oscillations And Waves From Basics To Modernity written by Lev Ostrovsky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-23 with Mathematics categories.

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.