Asymptotic Perturbation Theory Of Waves

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Asymptotic Perturbation Theory Of Waves

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Author : Lev Ostrovsky
Publisher : World Scientific
ISBN 13 : 178326473X
Total Pages : 227 pages
Book Rating : 4.7/5 (832 download)

Book Synopsis Asymptotic Perturbation Theory Of Waves by : Lev Ostrovsky

Download or read book Asymptotic Perturbation Theory Of Waves written by Lev Ostrovsky and published by World Scientific. This book was released on 2014-09-23 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher :
ISBN 13 : 9781848162358
Total Pages : 228 pages
Book Rating : 4.1/5 (623 download)

Book Synopsis Asymptotic Perturbation Theory of Waves by : Lev Ostrovsky

Download or read book Asymptotic Perturbation Theory of Waves written by Lev Ostrovsky and published by . This book was released on 2014-05-26 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Imperial College Press
ISBN 13 : 9781848162365
Total Pages : 300 pages
Book Rating : 4.1/5 (623 download)

Book Synopsis Perturbation Theories, Evolution Equations, and Solitons by : Konstantin Gorshkov

Download or read book Perturbation Theories, Evolution Equations, and Solitons written by Konstantin Gorshkov and published by Imperial College Press. This book was released on 2014 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Pitman Advanced Publishing Program
ISBN 13 :
Total Pages : 282 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Asymptotic Methods in Nonlinear Wave Theory by : Alan Jeffrey

Download or read book Asymptotic Methods in Nonlinear Wave Theory written by Alan Jeffrey and published by Pitman Advanced Publishing Program. This book was released on 1982 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics

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Author : John P. Boyd
Publisher : Springer Science & Business Media
ISBN 13 : 1461558255
Total Pages : 609 pages
Book Rating : 4.4/5 (615 download)

Book Synopsis Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics by : John P. Boyd

Download or read book Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics written by John P. Boyd and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Asymptotic Perturbation Methods

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Author : Attilio Maccari
Publisher : John Wiley & Sons
ISBN 13 : 3527841733
Total Pages : 261 pages
Book Rating : 4.5/5 (278 download)

Book Synopsis Asymptotic Perturbation Methods by : Attilio Maccari

Download or read book Asymptotic Perturbation Methods written by Attilio Maccari and published by John Wiley & Sons. This book was released on 2023-01-10 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Asymptotic Wave Theory

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Author : Maurice Roseau
Publisher : Elsevier
ISBN 13 : 0444601910
Total Pages : 360 pages
Book Rating : 4.4/5 (446 download)

Book Synopsis Asymptotic Wave Theory by : Maurice Roseau

Download or read book Asymptotic Wave Theory written by Maurice Roseau and published by Elsevier. This book was released on 2012-12-02 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Wave Theory investigates the asymptotic behavior of wave representations and presents some typical results borrowed from hydrodynamics and elasticity theory. It describes techniques such as Fourier-Laplace transforms, operational calculus, special functions, and asymptotic methods. It also discusses applications to the wave equation, the elements of scattering matrix theory, problems related to the wave equation, and diffraction. Organized into eight chapters, this volume begins with an overview of the Fourier-Laplace integral, the Mellin transform, and special functions such as the gamma function and the Bessel functions. It then considers wave propagation, with emphasis on representations of plane, cylindrical or spherical waves. It methodically introduces the reader to the reflexion and refraction of a plane wave at the interface between two homogeneous media, the asymptotic expansion of Hankel's functions in the neighborhood of the point at infinity, and the asymptotic behavior of the Laplace transform. The book also examines the method of steepest descent, the asymptotic representation of Hankel's function of large order, and the scattering matrix theory. The remaining chapters focus on problems of flow in open channels, the propagation of elastic waves within a layered spherical body, and some problems in water wave theory. This book is a valuable resource for mechanics and students of applied mathematics and mechanics.

Nonlinear Dispersive Waves

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Author : Mark J. Ablowitz
Publisher : Cambridge University Press
ISBN 13 : 1139503480
Total Pages : 363 pages
Book Rating : 4.1/5 (395 download)

Book Synopsis Nonlinear Dispersive Waves by : Mark J. Ablowitz

Download or read book Nonlinear Dispersive Waves written by Mark J. Ablowitz and published by Cambridge University Press. This book was released on 2011-09-08 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Asymptotic Methods

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Author : David Y. Gao
Publisher : CRC Press
ISBN 13 : 1420011731
Total Pages : 270 pages
Book Rating : 4.4/5 (2 download)

Book Synopsis Introduction to Asymptotic Methods by : David Y. Gao

Download or read book Introduction to Asymptotic Methods written by David Y. Gao and published by CRC Press. This book was released on 2006-05-03 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Large-omega Asymptotic Expansions and Perturbation Theory for the Harmonic Oscillator

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Author : G. R. Osche
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.:/5 (227 download)

Book Synopsis Large-omega Asymptotic Expansions and Perturbation Theory for the Harmonic Oscillator by : G. R. Osche

Download or read book Large-omega Asymptotic Expansions and Perturbation Theory for the Harmonic Oscillator written by G. R. Osche and published by . This book was released on 1970 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Part I, a large parameter asymptotic expansion of a perturbed simple harmonic oscillator is presented. Perturbations of the form lambda (x sup alpha) are studied where lambda is the coupling constant. The method is demonstrated by a general derivation of the wave functions to third order for any alpha and quantum number n. Additional expressions are presented for the ground states to tenth order in the energy. It is also shown that the matching condition for the basic and perturbation theory solutions is automatically satisfied due to the non-singular nature of the perturbation. In Part II, the solution to the Schrodinger equation for a one dimensional harmonic oscillator under the influence of two general classes of potentials is investigated using high-order perturbation theory. It is shown that by utilizing a finite expansion of the perturbation theory wave function in terms of Hermite polynomials, perturbation theory results can be readily obtained, for any state, to arbitrarily high order. (Author).

Methods and Applications of Singular Perturbations

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Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
ISBN 13 : 0387283137
Total Pages : 332 pages
Book Rating : 4.3/5 (872 download)

Book Synopsis Methods and Applications of Singular Perturbations by : Ferdinand Verhulst

Download or read book Methods and Applications of Singular Perturbations written by Ferdinand Verhulst and published by Springer Science & Business Media. This book was released on 2006-06-04 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach

Singular Perturbations and Asymptotics

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Author : Richard E. Meyer
Publisher : Academic Press
ISBN 13 : 1483264572
Total Pages : 418 pages
Book Rating : 4.4/5 (832 download)

Book Synopsis Singular Perturbations and Asymptotics by : Richard E. Meyer

Download or read book Singular Perturbations and Asymptotics written by Richard E. Meyer and published by Academic Press. This book was released on 2014-05-10 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Research Center Symposia and Advanced Seminar Series: Singular Perturbations and Asymptotics covers the lectures presented at an Advanced Seminar on Singular Perturbation and Asymptotics, held in Madison, Wisconsin on May 28-30, 1980 under the auspices of the Mathematics Research Center of the University of Wisconsin—Madison. The book focuses on the processes, methodologies, reactions, and principles involved in singular perturbations and asymptotics, including boundary value problems, equations, perturbations, water waves, and gas dynamics. The selection first elaborates on basic concepts in the analysis of singular perturbations, limit process expansions and approximate equations, and results on singularly perturbed boundary value problems. Discussions focus on quasi-linear and nonlinear problems, semilinear systems, water waves, expansion in gas dynamics, asymptotic matching principles, and classical perturbation analysis. The text then takes a look at multiple solutions of singularly perturbed systems in the conditionally stable case and singular perturbations, stochastic differential equations, and applications. The book ponders on connection problems in the parameterless case; general connection-formula problem for linear differential equations of the second order; and turning-point problems for ordinary differential equations of hydrodynamic type. Topics include the comparison equation method, boundary layer flows, compound matrix method, asymptotic solution of the connection-formula problem, and higher order equations. The selection is a valuable source of information for researchers interested in singular perturbations and asymptotics.

Problems in Singular Perturbation Theory

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Author : James Alan Cochran
Publisher :
ISBN 13 :
Total Pages : 204 pages
Book Rating : 4.F/5 ( download)

Book Synopsis Problems in Singular Perturbation Theory by : James Alan Cochran

Download or read book Problems in Singular Perturbation Theory written by James Alan Cochran and published by . This book was released on 1962 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Perturbation Methods

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Author : Mark H. Holmes
Publisher : Springer Science & Business Media
ISBN 13 : 1461253470
Total Pages : 344 pages
Book Rating : 4.4/5 (612 download)

Book Synopsis Introduction to Perturbation Methods by : Mark H. Holmes

Download or read book Introduction to Perturbation Methods written by Mark H. Holmes and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Slowly Varying Oscillations And Waves: From Basics To Modernity

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Author : Lev Ostrovsky
Publisher : World Scientific
ISBN 13 : 9811247501
Total Pages : 372 pages
Book Rating : 4.8/5 (112 download)

Book Synopsis Slowly Varying Oscillations And Waves: From Basics To Modernity by : Lev Ostrovsky

Download or read book Slowly Varying Oscillations And Waves: From Basics To Modernity written by Lev Ostrovsky and published by World Scientific. This book was released on 2022-02-23 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Perturbation Theory for the Schrödinger Operator with a Periodic Potential

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Author : Yulia E. Karpeshina
Publisher : Springer
ISBN 13 : 3540691561
Total Pages : 358 pages
Book Rating : 4.5/5 (46 download)

Book Synopsis Perturbation Theory for the Schrödinger Operator with a Periodic Potential by : Yulia E. Karpeshina

Download or read book Perturbation Theory for the Schrödinger Operator with a Periodic Potential written by Yulia E. Karpeshina and published by Springer. This book was released on 2006-11-14 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Asymptotic Methods and Singular Perturbations

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Author : Robert E. O'Malley
Publisher : American Mathematical Soc.
ISBN 13 : 9780821813300
Total Pages : 164 pages
Book Rating : 4.8/5 (133 download)

Book Synopsis Asymptotic Methods and Singular Perturbations by : Robert E. O'Malley

Download or read book Asymptotic Methods and Singular Perturbations written by Robert E. O'Malley and published by American Mathematical Soc.. This book was released on 1976 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: