Analytical Methods For Nonlinear Oscillators And Solitary Waves

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Analytical Methods for Nonlinear Oscillators and Solitary Waves

Author : Chu-Hui He
Publisher : Frontiers Media SA
ISBN 13 : 2832539637
Total Pages : 132 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis Analytical Methods for Nonlinear Oscillators and Solitary Waves by : Chu-Hui He

Download or read book Analytical Methods for Nonlinear Oscillators and Solitary Waves written by Chu-Hui He and published by Frontiers Media SA. This book was released on 2023-11-24 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most well-known analytical method is the perturbation method, which has led to the great discovery of Neptune in 1846, and since then mathematical prediction and empirical observation became two sides of a coin in physics. However, the perturbation method is based on the small parameter assumption, and the obtained solutions are valid only for weakly nonlinear equations, which have greatly limited their applications to modern physical problems. To overcome the shortcomings, many mathematicians and physicists have been extensively developing various technologies for several centuries, however, there is no universal method for all nonlinear problems, and mathematical prediction with remarkably high accuracy is still much needed for modern physics, for example, the solitary waves traveling along an unsmooth boundary, the low-frequency property of a harvesting energy device, the pull-in voltage in a micro-electromechanical system. Now various effective analytical methods have appeared in the open literature, e.g., the homotopy perturbation method and the variational iteration method. An analytical solution provides a fast insight into its physical properties of a practical problem, e.g., frequency-amplitude relation of a nonlinear oscillator, solitary wave in an optical fiber, pull-in instability of a microelectromechanical system, making mathematical prediction even more attractive in modern physics. Nonlinear physics has been developing into a new stage, where the fractal-fractional differential equations have to be adopted to describe more accurately discontinuous problems, and it becomes ever more difficult to find an analytical solution for such nonlinear problems, and the analytical methods for fractal-fractional differential equations have laid the foundations for nonlinear physics.

Normal Modes and Localization in Nonlinear Systems

Author : Alexander F. Vakakis
Publisher : John Wiley & Sons
ISBN 13 : 3527617876
Total Pages : 552 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis Normal Modes and Localization in Nonlinear Systems by : Alexander F. Vakakis

Download or read book Normal Modes and Localization in Nonlinear Systems written by Alexander F. Vakakis and published by John Wiley & Sons. This book was released on 2008-07-11 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This landmark book deals with nonlinear normal modes (NNMs) and nonlinear mode localization. Offers an analysis which enables the study of various nonlinear phenomena having no counterpart in linear theory. On a more theoretical level, the concept of NNMs will be shown to provide an excellent framework for understanding a variety of distinctively nonlinear phenomena such as mode bifurcations and standing or traveling solitary waves.

Nonlinear Oscillations

Author : Ali H. Nayfeh
Publisher : John Wiley & Sons
ISBN 13 : 3527617590
Total Pages : 720 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis Nonlinear Oscillations by : Ali H. Nayfeh

Download or read book Nonlinear Oscillations written by Ali H. Nayfeh and published by John Wiley & Sons. This book was released on 2008-09-26 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses simple physical examples to explain nonlinear dispersive and nondispersive waves. The notation is unified and the analysis modified to conform to discussions. Solutions are worked out in detail for numerous examples, results are plotted and explanations are couched in physical terms. The book contains an extensive bibliography.

Los Alamos Science

Author :
Publisher :
ISBN 13 :
Total Pages : 332 pages
Book Rating : 4.3/5 ( download)

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Book Synopsis Los Alamos Science by :

Download or read book Los Alamos Science written by and published by . This book was released on 1987 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stanislaw Ulam 1909-1984

Author :
Publisher :
ISBN 13 :
Total Pages : 326 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Stanislaw Ulam 1909-1984 by :

Download or read book Stanislaw Ulam 1909-1984 written by and published by . This book was released on 1987 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:

From Cardinals to Chaos

Author : N. G. Cooper
Publisher : CUP Archive
ISBN 13 : 9780521367349
Total Pages : 324 pages
Book Rating : 4.3/5 (673 download)

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Book Synopsis From Cardinals to Chaos by : N. G. Cooper

Download or read book From Cardinals to Chaos written by N. G. Cooper and published by CUP Archive. This book was released on 1989-02-24 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published 1987 as Los Alamos science, special issue. A compendium of biographical (and autobiographical) notes, essays, and scientific articles reflecting on Ulam's legacy of interdisciplinary approaches to problems in math, physics, and biology; and previously unpublished miscellanea--conversations, a satirical play. The whole serves to celebrate the personality and contributions of the dynamic mathematician. Annotation copyrighted by Book News, Inc., Portland, OR

Nonlinear Dirac Equation

Author : Nabile Boussaïd
Publisher :
ISBN 13 : 9781470454227
Total Pages : 297 pages
Book Rating : 4.4/5 (542 download)

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Book Synopsis Nonlinear Dirac Equation by : Nabile Boussaïd

Download or read book Nonlinear Dirac Equation written by Nabile Boussaïd and published by . This book was released on 1920 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves. The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrödinger equation. It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves the general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation

Travelling Waves And Periodic Oscillations In Fermi-pasta-ulam Lattices

Author : Alexander Pankov
Publisher : World Scientific
ISBN 13 : 178326036X
Total Pages : 212 pages
Book Rating : 4.7/5 (832 download)

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Book Synopsis Travelling Waves And Periodic Oscillations In Fermi-pasta-ulam Lattices by : Alexander Pankov

Download or read book Travelling Waves And Periodic Oscillations In Fermi-pasta-ulam Lattices written by Alexander Pankov and published by World Scientific. This book was released on 2005-03-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique book that presents rigorous mathematical results on Fermi-Pasta-Ulam lattices, a field of great interest in nonlinear analysis, nonlinear science, mathematical physics, etc. It considers travelling waves and time periodic oscillations in infinite Fermi-Pasta-Ulam lattices, which are not necessarily spatially homogenous. Similar systems, infinite chains of linearly coupled nonlinear oscillators, are also discussed. The book is self-contained and includes a number of open problems, making it suitable for use in a course for graduate students./a

Applied mechanics reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 400 pages
Book Rating : 4.3/5 (243 download)

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Book Synopsis Applied mechanics reviews by :

Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Solitary Waves in Dispersive Complex Media

Author : Vasiliĭ I︠U︡rʹevich Belashov
Publisher : Springer Science & Business Media
ISBN 13 : 9783540233763
Total Pages : 316 pages
Book Rating : 4.2/5 (337 download)

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Book Synopsis Solitary Waves in Dispersive Complex Media by : Vasiliĭ I︠U︡rʹevich Belashov

Download or read book Solitary Waves in Dispersive Complex Media written by Vasiliĭ I︠U︡rʹevich Belashov and published by Springer Science & Business Media. This book was released on 2005-01-19 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to one of the most interesting and rapidly developing areas of modern nonlinear physics and mathematics - the theoretical, analytical and advanced numerical, study of the structure and dynamics of one-dimensional as well as two- and three-dimensional solitons and nonlinear waves described by Korteweg-de Vries (KdV), Kadomtsev-Petviashvili (KP), nonlinear Schrödinger (NLS) and derivative NLS (DNLS) classes of equations. Special attention is paid to generalizations (relevant to various complex physical media) of these equations, accounting for higher-order dispersion corrections, influence of dissipation, instabilities, and stochastic fluctuations of the wave fields. The book addresses researchers working in the theory and numerical simulations of dispersive complex media in such fields as hydrodynamics, plasma physics, and aerodynamics. It will also be useful as a reference work for graduate students in physics and mathematics.

Selected Topics in Nonlinear Wave Mechanics

Author : C.I. Christov
Publisher : Springer Science & Business Media
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Selected Topics in Nonlinear Wave Mechanics by : C.I. Christov

Download or read book Selected Topics in Nonlinear Wave Mechanics written by C.I. Christov and published by Springer Science & Business Media. This book was released on 2002 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive reference text gives an overview of the current state of nonlinear wave mechanics in both elastic and fluid media. Consisting of self-contained chapters, the book covers new aspects on strong discontinuities (shock waves) and localized self- preserving (permanent) shapes (solitary waves and solitons). Special attention is devoted to the kinematics and dynamics of permanent waves when dissipative effects are added to the original balance between nonlinearity and dispersion. Key features include: * survey chapters written in an accessible style by leading specialists * coverage of emerging topics in the field * interdisciplinary approach integrating mathematical theory and physical applications of nonlinear waves in elastic and fluid media * treatment of the intrinsic mechanisms of propagation of different types of nonlinear waves * presentation of analytical methods for solving wave propagation problems in elastic and fluid media * user-friendly index 'Selected Topics in Nonlinear Wave Mechanics' provides readers with recent developments in the nonlinear propagation and scattering of waves in both elastic solids and liquids. The book is useful for applied mathematicians, physicists, mechanical, civil and aerospace engineers, as well as graduate students in those fields. Contributors: R.M. Axel, C.I. Christov, A. Guran, J.B. Haddow, G.A. Maugin, A. Morro, A. Nagl, P.K. Newton, A.V. Porubov, R.J. Tait, H. sberall, M.G. Velarde, W.B. Zimmerman.

Nonlinear Dispersive Waves

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

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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.

Solitons

Author : Mohamed Atef Helal
Publisher : Springer Nature
ISBN 13 : 1071624571
Total Pages : 483 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Solitons by : Mohamed Atef Helal

Download or read book Solitons written by Mohamed Atef Helal and published by Springer Nature. This book was released on 2022-11-12 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: This newly updated volume of the Encyclopedia of Complexity and Systems Science (ECSS) presents several mathematical models that describe this physical phenomenon, including the famous non-linear equation Korteweg-de-Vries (KdV) that represents the canonical form of solitons. Also, there exists a class of nonlinear partial differential equations that led to solitons, e.g., Kadomtsev-Petviashvili (KP), Klein-Gordon (KG), Sine-Gordon (SG), Non-Linear Schrödinger (NLS), Korteweg-de-Vries Burger’s (KdVB), etc. Different linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Other non-analytic methods use the computational techniques available in such popular mathematical packages as Mathematica, Maple, and MATLAB. The main purpose of this volume is to provide physicists, engineers, and their students with the proper methods and tools to solve the soliton equations, and to discover the new possibilities of using solitons in multi-disciplinary areas ranging from telecommunications to biology, cosmology, and oceanographic studies.

Nonlinear Waves in Integrable and Nonintegrable Systems

Author : Jianke Yang
Publisher : SIAM
ISBN 13 : 0898719682
Total Pages : 453 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Nonlinear Waves in Integrable and Nonintegrable Systems by : Jianke Yang

Download or read book Nonlinear Waves in Integrable and Nonintegrable Systems written by Jianke Yang and published by SIAM. This book was released on 2010-01-01 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind.

Wave Propagation in Linear and Nonlinear Periodic Media

Author : Francesco Romeo
Publisher : Springer Science & Business Media
ISBN 13 : 3709113091
Total Pages : 332 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Wave Propagation in Linear and Nonlinear Periodic Media by : Francesco Romeo

Download or read book Wave Propagation in Linear and Nonlinear Periodic Media written by Francesco Romeo and published by Springer Science & Business Media. This book was released on 2013-07-30 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Waves and defect modes in structures media.- Piezoelectric superlattices and shunted periodic arrays as tunable periodic structures and metamaterials.- Topology optimization.- Map-based approaches for periodic structures.- Methodologies for nonlinear periodic media. The contributions in this volume present both the theoretical background and an overview of the state-of-the art in wave propagation in linear and nonlinear periodic media in a consistent format. They combine the material issued from a variety of engineering applications, spanning a wide range of length scale, characterized by structures and materials, both man-made and naturally occurring, featuring geometry, micro-structural and/or materials properties that vary periodically in space, including periodically stiffened plates, shells and beam-like as well as bladed disc assemblies, phononic metamaterials, photonic crystals and ordered granular media. Along with linear models and applications, analytical methodologies for analyzing and exploiting complex dynamical phenomena arising in nonlinear periodic systems are also presented.

Nonlinear Waves

Author : Lokenath Debnath
Publisher : Cambridge University Press
ISBN 13 : 0511868618
Total Pages : 372 pages
Book Rating : 4.5/5 (118 download)

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Book Synopsis Nonlinear Waves by : Lokenath Debnath

Download or read book Nonlinear Waves written by Lokenath Debnath and published by Cambridge University Press. This book was released on 2009-01-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.

Strong Nonlinear Oscillators

Author : Livija Cveticanin
Publisher : Springer
ISBN 13 : 9783319864846
Total Pages : 317 pages
Book Rating : 4.8/5 (648 download)

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Book Synopsis Strong Nonlinear Oscillators by : Livija Cveticanin

Download or read book Strong Nonlinear Oscillators written by Livija Cveticanin and published by Springer. This book was released on 2018-08-04 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. It presents the author’s original method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameters is considered. In this second edition of the book, the number of approximate solving procedures for strong nonlinear oscillators is enlarged and a variety of procedures for solving free strong nonlinear oscillators is suggested. A method for error estimation is also given which is suitable to compare the exact and approximate solutions. Besides the oscillators with one degree-of-freedom, the one and two mass oscillatory systems with two-degrees-of-freedom and continuous oscillators are considered. The chaos and chaos suppression in ideal and non-ideal mechanical systems is explained. In this second edition more attention is given to the application of the suggested methodologies and obtained results to some practical problems in physics, mechanics, electronics and biomechanics. Thus, for the oscillator with two degrees-of-freedom, a generalization of the solving procedure is performed. Based on the obtained results, vibrations of the vocal cord are analyzed. In the book the vibration of the axially purely nonlinear rod as a continuous system is investigated. The developed solving procedure and the solutions are applied to discuss the muscle vibration. Vibrations of an optomechanical system are analyzed using the oscillations of an oscillator with odd or even quadratic nonlinearities. The extension of the forced vibrations of the system is realized by introducing the Ateb periodic excitation force which is the series of a trigonometric function. The book is self-consistent and suitable for researchers and as a textbook for students and also professionals and engineers who apply these techniques to the field of nonlinear oscillations.