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Author : Georgy Omel'yanov
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (115 download)
Download or read book A Perturbation Theory for Nonintegrable Equations with Small Dispersion written by Georgy Omel'yanov and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ricardo Lopez-Ruiz
Publisher : BoD – Books on Demand
ISBN 13 : 1789230500
Total Pages : 204 pages
Book Rating : 4.7/5 (892 download)
Download or read book Complexity in Biological and Physical Systems written by Ricardo Lopez-Ruiz and published by BoD – Books on Demand. This book was released on 2018-05-02 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and simulating biological and physical systems are nowadays active branches of science. The diversity and complexity of behaviors and patterns present in the natural world have their reciprocity in life systems. Bifurcations, solitons and fractals are some of these ubiquitous structures that can be indistinctively identified in many models with the most diverse applications, from microtubules with an essential role in the maintenance and the shaping of cells, to the nano/microscale structure in disordered systems determined with small-angle scattering techniques. This book collects several works in this direction, giving an overview of some models and theories, which are useful for the study and analysis of complex biological and physical systems. It can provide a good guidance for physicists with interest in biology, applied research scientists and postgraduate students.
Author : Jianke Yang
Publisher : SIAM
ISBN 13 : 0898719682
Total Pages : 453 pages
Book Rating : 4.8/5 (987 download)
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.
Author : Michael Oberguggenberger
Publisher : Birkhäuser
ISBN 13 : 3319519115
Total Pages : 280 pages
Book Rating : 4.3/5 (195 download)
Download or read book Generalized Functions and Fourier Analysis written by Michael Oberguggenberger and published by Birkhäuser. This book was released on 2017-05-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis. The volume is a collection of chapters addressing these fields, their interaction, their unifying concepts and their applications and is based on scientific activities related to the International Association for Generalized Functions (IAGF) and the ISAAC interest groups on Pseudo-Differential Operators (IGPDO) and on Generalized Functions (IGGF), notably on the longstanding collaboration of these groups within ISAAC.
Author : Lev Ostrovsky
Publisher : World Scientific
ISBN 13 : 178326473X
Total Pages : 227 pages
Book Rating : 4.7/5 (832 download)
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.
Author : William Rees Sears
Publisher :
ISBN 13 : 9780691626024
Total Pages : 0 pages
Book Rating : 4.6/5 (26 download)
Download or read book Small Perturbation Theory written by William Rees Sears and published by . This book was released on 2015-12-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cover -- Contents
Author : James Alan Cochran
Publisher :
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.F/5 ( download)
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 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : L. G. Napolitano
Publisher :
ISBN 13 :
Total Pages : 98 pages
Book Rating : 4.:/5 (227 download)
Download or read book Small Perturbation Theories for Singly Reacting Mixtures written by L. G. Napolitano and published by . This book was released on 1968 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report presents the linear and non-linear (i.e. transonic) small perturbation theory for non-equilibrium plane flows. In particular, three different transonic regimes for a singly reacting mixture are defined and the appropriate forms of the corresponding potential equations are derived, interpreted and discussed, especially in connection with their presumable range of uniform validity in the physical space. Seven new types of potential equations are obtained, two linear and the other non linear and of the mixed type. The formal derivation of these equations is implemented by a derivation based on physical interpretations of the contributions given to the kinetic energy and excess power balance equations by the several phenomena occurring during a dynamical evolution of a gas mixture in the presence of rate processes. (Author).
Author : Jianke Yang
Publisher : SIAM
ISBN 13 : 0898717051
Total Pages : 452 pages
Book Rating : 4.8/5 (987 download)
Download or read book Nonlinear Waves in Integrable and Non-integrable Systems written by Jianke Yang and published by SIAM. This book was released on 2010-12-02 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Waves in Integrable and Nonintegrable Systems 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. This book is intended for researchers and graduate students working in applied mathematics and various physical subjects where nonlinear wave phenomena arise (such as nonlinear optics, Bose-Einstein condensates, and fluid dynamics).
Author :
Publisher :
ISBN 13 :
Total Pages : 29 pages
Book Rating : 4.:/5 (227 download)
Download or read book Perturbation Theory for the - Benjamin-Ono Equation written by and published by . This book was released on 1998 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a perturbation theory for the Benjamin-Ono (BO) equation. This perturbation theory is based on the Inverse Scattering Transform for the BO equation which was originally developed by Fokas and Ablowitz and recently refined by Kaup and Matsuno. We find the expressions for the variations of the scattering data with respect to the potential, as well as the dual expression for the variation of the potential in terms of the variations of the scattering data. This allows us to introduce the squared eigenfunctions for the BO equation, whose completeness and orthogonality in both chi- and lambda-spaces we also establish. We consider the two most important applications of the developed machinery. First we present an explicit first-order solution of the BO equation driven by a small perturbation. Second we introduce the Poisson bracket and a set of the canonical action-angle variables for the BO equation and thus demonstrate its complete integrability as a Hamiltonian dynamical system.
Author : M. V. Karasev
Publisher : American Mathematical Soc.
ISBN 13 : 9780821833360
Total Pages : 298 pages
Book Rating : 4.8/5 (333 download)
Download or read book Asymptotic Methods for Wave and Quantum Problems written by M. V. Karasev and published by American Mathematical Soc.. This book was released on 2003 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection consists of four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of quantum and wave problems. In the introductory paper ``Quantization and Intrinsic Dynamics'' a relationship between quantization of symplectic manifolds and nonlinear wave equations is described and discussed from the viewpoint of the weak asymptotics method (asymptotics in distributions) and the semiclassical approximation method. It also explains a hidden dynamic geometry that arises when using these methods. Three other papers discuss applications of asymptotic methods to the construction of wave-type solutions of nonlinear PDE's, to the theory of semiclassical approximation (in particular, the Whitham method) for nonlinear second-order ordinary differential equations, and to the study of the Schrodinger type equations whose potential wells are sufficiently shallow that the discrete spectrum contains precisely one point. All the papers contain detailed references and are oriented not only to specialists in asymptotic methods, but also to a wider audience of researchers and graduate students working in partial differential equations and mathematical physics.
Author : H. F. Tiersten
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (227 download)
Download or read book Perturbation Theory for Linear Electroelastic Equations for Small Fields Superposed on a Bias written by H. F. Tiersten and published by . This book was released on 1977 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: A perturbation formulation of the equations of linear piezoelectricity for small fields superposed on a bias is obtained from a Green's function representation. It is shown that the resulting equation for the first perturbation of the eigenvalue may be obtained without the use of a Green's tensor or a complete set of orthogonal eigensolutions. Since the bias enters the constitutive equations, the boundary conditions contain perturbation terms as well as the differential equations. The linear electroelastic equations for small fields superposed on a bias differ from the equations of linear piezoelectricity because the effective material constants of linear electroelasticity have less symmetry than the constants of linear piezoelectricity. Consequently, a perturbation formulation of the linear electroelastic equations for small fields superposed on a bias is presented. It is shown that the effective constants of linear electroelasticity have just the symmetry required for the condition of the orthogonality of linear electroelastic vibrations to hold. (Author).
Author : Vladimir Georgiev
Publisher : Springer Nature
ISBN 13 : 9811964343
Total Pages : 246 pages
Book Rating : 4.8/5 (119 download)
Download or read book Qualitative Properties of Dispersive PDEs written by Vladimir Georgiev and published by Springer Nature. This book was released on 2022-12-02 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a valuable collection of contributions by distinguished scholars presenting the state of the art and some of the most significant latest developments and future challenges in the field of dispersive partial differential equations. The material covers four major lines: (1) Long time behaviour of NLS-type equations, (2) probabilistic and nonstandard methods in the study of NLS equation, (3) dispersive properties for heat-, Schrödinger-, and Dirac-type flows, (4) wave and KdV-type equations. Across a variety of applications an amount of crucial mathematical tools are discussed, whose applicability and versatility goes beyond the specific models presented here. Furthermore, all contributions include updated and comparative literature.
Author : Mário F. S. Ferreira
Publisher : Springer Nature
ISBN 13 : 3030974936
Total Pages : 369 pages
Book Rating : 4.0/5 (39 download)
Download or read book Dissipative Optical Solitons written by Mário F. S. Ferreira and published by Springer Nature. This book was released on 2022-09-23 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the basic concept of a dissipative soliton, before going to explore recent theoretical and experimental results for various classes of dissipative optical solitons, high-energy dissipative solitons and their applications, and mode-locked fiber lasers. A soliton is a concept which describes various physical phenomena ranging from solitary waves forming on water to ultrashort optical pulses propagating in an optical fiber. While solitons are usually attributed to integrability, in recent years the notion of a soliton has been extended to various systems which are not necessarily integrable. Until now, the main emphasis has been given to well-known conservative soliton systems, but new avenues of inquiry were opened when physicists realized that solitary waves did indeed exist in a wide range of non-integrable and non-conservative systems leading to the concept of so-called dissipative optical solitons. Dissipative optical solitons have many unique properties which differ from those of their conservative counterparts. For example, except for very few cases, they form zero-parameter families and their properties are completely determined by the external parameters of the optical system. They can exist indefinitely in time, as long as these parameters stay constant. These features of dissipative solitons are highly desirable for several applications, such as in-line regeneration of optical data streams and generation of stable trains of laser pulses by mode-locked cavities.
Author : G. F. Roach
Publisher : Princeton University Press
ISBN 13 : 0691142173
Total Pages : 399 pages
Book Rating : 4.6/5 (911 download)
Download or read book Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics written by G. F. Roach and published by Princeton University Press. This book was released on 2012-03-04 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory. Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians.
Author : Andrei V. Gaponov-Grekhov
Publisher : Springer Science & Business Media
ISBN 13 : 3642753086
Total Pages : 337 pages
Book Rating : 4.6/5 (427 download)
Download or read book Nonlinear Waves 3 written by Andrei V. Gaponov-Grekhov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1972 the Schools on Nonlinear Physics in Gorky have been a meeting place for Soviet Scientists working in this field. Since 1989 the proceedings appear in English. They present a good cross section of nonlinear physics in the USSR. This third volume emerged from material presented at the 1989 School. It contains sections dealing with nonlinear problems in physics and astrophysics, quantum and solid state physics, dynamical chaos and self-organization.
Author : Lokenath Debnath
Publisher : CUP Archive
ISBN 13 : 9780521254687
Total Pages : 376 pages
Book Rating : 4.2/5 (546 download)
Download or read book Nonlinear Waves written by Lokenath Debnath and published by CUP Archive. This book was released on 1983-12-30 with total page 376 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.
