Nonlinear Oscillations Of Hamiltonian Pdes

Author : Massimiliano Berti
Publisher : Springer Science & Business Media
Page : 191 pages
File Size : 45,7 Mb
Release : 2007-10-01
Category : Mathematics
ISBN : 9780817646806

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Nonlinear Oscillations of Hamiltonian PDEs by Massimiliano Berti Pdf

Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations. The text serves as an introduction to research in this fascinating and rapidly growing field. Graduate students and researchers interested in variational techniques and nonlinear analysis applied to Hamiltonian PDEs will find inspiration in the book.

Author : Solomon Lefschetz
Publisher : Princeton University Press
Page : 224 pages
File Size : 53,5 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881758

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Contributions to the Theory of Nonlinear Oscillations (AM-41), Volume IV by Solomon Lefschetz Pdf

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-41), Volume IV, will be forthcoming.

Author : Solomon Lefschetz
Publisher : Princeton University Press
Page : 360 pages
File Size : 46,5 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882632

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Contributions to the Theory of Nonlinear Oscillations (AM-20), Volume I by Solomon Lefschetz Pdf

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-20), Volume I, will be forthcoming.

Author : Solomon Lefschetz,G. Seifert
Publisher : Princeton University Press
Page : 299 pages
File Size : 41,8 Mb
Release : 2024-06-16
Category : Nonlinear oscillations
ISBN : 9780691079110

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Contributions to the Theory of Nonlinear Oscillations by Solomon Lefschetz,G. Seifert Pdf

The book description for the forthcoming "Contributions to the Theory of Nonlinear Oscillations (AM-36)" is not yet available.

Author : P.S Landa
Publisher : Springer Science & Business Media
Page : 550 pages
File Size : 43,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401587631

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Nonlinear Oscillations and Waves in Dynamical Systems by P.S Landa Pdf

A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.

Author : Solomon Lefschetz,Lamberto Cesari
Publisher : Unknown
Page : 310 pages
File Size : 42,7 Mb
Release : 1960
Category : Oscillations
ISBN : STANFORD:36105002015688

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Contributions to the Theory of Nonlinear Oscillations by Solomon Lefschetz,Lamberto Cesari Pdf

Author : Maurizio Garrione,Filippo Gazzola
Publisher : Springer Nature
Page : 115 pages
File Size : 52,6 Mb
Release : 2019-10-31
Category : Mathematics
ISBN : 9783030302184

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Nonlinear Equations for Beams and Degenerate Plates with Piers by Maurizio Garrione,Filippo Gazzola Pdf

This book develops a full theory for hinged beams and degenerate plates with multiple intermediate piers with the final purpose of understanding the stability of suspension bridges. New models are proposed and new tools are provided for the stability analysis. The book opens by deriving the PDE’s based on the physical models and by introducing the basic framework for the linear stationary problem. The linear analysis, in particular the behavior of the eigenvalues as the position of the piers varies, enables the authors to tackle the stability issue for some nonlinear evolution beam equations, with the aim of determining the “best position” of the piers within the beam in order to maximize its stability. The study continues with the analysis of a class of degenerate plate models. The torsional instability of the structure is investigated, and again, the optimal position of the piers in terms of stability is discussed. The stability analysis is carried out by means of both analytical tools and numerical experiments. Several open problems and possible future developments are presented. The qualitative analysis provided in the book should be seen as the starting point for a precise quantitative study of more complete models, taking into account the action of aerodynamic forces. This book is intended for a two-fold audience. It is addressed both to mathematicians working in the field of Differential Equations, Nonlinear Analysis and Mathematical Physics, due to the rich number of challenging mathematical questions which are discussed and left as open problems, and to Engineers interested in mechanical structures, since it provides the theoretical basis to deal with models for the dynamics of suspension bridges with intermediate piers. More generally, it may be enjoyable for readers who are interested in the application of Mathematics to real life problems.

Author : Philippe Guyenne,David Nicholls,Catherine Sulem
Publisher : Springer
Page : 449 pages
File Size : 41,9 Mb
Release : 2015-09-11
Category : Mathematics
ISBN : 9781493929504

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Hamiltonian Partial Differential Equations and Applications by Philippe Guyenne,David Nicholls,Catherine Sulem Pdf

This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.

Author : Walter Craig
Publisher : Springer Science & Business Media
Page : 441 pages
File Size : 51,6 Mb
Release : 2008-02-17
Category : Mathematics
ISBN : 9781402069642

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Hamiltonian Dynamical Systems and Applications by Walter Craig Pdf

This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.

Author : Peter Hagedorn
Publisher : Oxford University Press, USA
Page : 332 pages
File Size : 41,7 Mb
Release : 1988
Category : Language Arts & Disciplines
ISBN : UOM:39015054001725

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Non-linear Oscillations by Peter Hagedorn Pdf

A description of systems in terms of non-linear ordinary differential equations and an attempt to convey the basic ideas of the dynamic behaviour of non-linear systems, with a chapter on optimal control.

Author : Solomon Lefschetz
Publisher : Unknown
Page : 136 pages
File Size : 44,7 Mb
Release : 1952
Category : Oscillations
ISBN : UOM:39076007003333

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Contributions to the Theory of Nonlinear Oscillations [by] S. P. Diliberto [and Others] by Solomon Lefschetz Pdf

Author : Alexander Komech
Publisher : World Scientific
Page : 272 pages
File Size : 43,5 Mb
Release : 2022-02-18
Category : Science
ISBN : 9789811248917

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Lectures On Quantum Mechanics And Attractors by Alexander Komech Pdf

This book gives a concise introduction to Quantum Mechanics with a systematic, coherent, and in-depth explanation of related mathematical methods from the scattering theory and the theory of Partial Differential Equations.The book is aimed at graduate and advanced undergraduate students in mathematics, physics, and chemistry, as well as at the readers specializing in quantum mechanics, theoretical physics and quantum chemistry, and applications to solid state physics, optics, superconductivity, and quantum and high-frequency electronic devices.The book utilizes elementary mathematical derivations. The presentation assumes only basic knowledge of the origin of Hamiltonian mechanics, Maxwell equations, calculus, Ordinary Differential Equations and basic PDEs. Key topics include the Schrödinger, Pauli, and Dirac equations, the corresponding conservation laws, spin, the hydrogen spectrum, and the Zeeman effect, scattering of light and particles, photoelectric effect, electron diffraction, and relations of quantum postulates with attractors of nonlinear Hamiltonian PDEs. Featuring problem sets and accompanied by extensive contemporary and historical references, this book could be used for the course on Quantum Mechanics and is also suitable for individual study.

Author : Ronald E. Mickens
Publisher : World Scientific
Page : 261 pages
File Size : 42,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814291651

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Truly Nonlinear Oscillations by Ronald E. Mickens Pdf

This unique book provides a concise presentation of many of the fundamental strategies for calculating approximations to the oscillatory solutions of "truly nonlinear" (TNL) oscillator equations. The volume gives a general overview of the author's work on harmonic balance, iteration and combined linearization-averaging methods. However, full discussions are also presented on parameter expansion procedures and a first-order averaging technique for TNL oscillators. The calculational basis of each method is clarified by applying them to a set of standard TNL oscillator equations. This allows a direct comparison to be made among the various methods. The book is self-contained and therefore suitable for both classroom use and self-study by students and professionals who desire to learn, understand, and apply this technique to the field of nonlinear oscillations.

Author : M.I Rabinovich,D.I. Trubetskov
Publisher : Taylor & Francis
Page : 610 pages
File Size : 54,7 Mb
Release : 1989-11-30
Category : Gardening
ISBN : 0792304454

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Oscillations and Waves by M.I Rabinovich,D.I. Trubetskov Pdf

'Et mai *...* si j'avait su comment en revenir. One service mathematics has rendered the je n'y semis point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost sheJf next to the dusty canister Iabclled 'discarded non· The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com­ puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Author : Sergej B. Kuksin
Publisher : Clarendon Press
Page : 228 pages
File Size : 52,6 Mb
Release : 2000
Category : Mathematics
ISBN : 0198503954

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Analysis of Hamiltonian PDEs by Sergej B. Kuksin Pdf

For the last 20-30 years, interest among mathematicians and physicists in infinite-dimensional Hamiltonian systems and Hamiltonian partial differential equations has been growing strongly, and many papers and a number of books have been written on integrable Hamiltonian PDEs. During the last decade though, the interest has shifted steadily towards non-integrable Hamiltonian PDEs. Here, not algebra but analysis and symplectic geometry are the appropriate analysing tools. The present book is the first one to use this approach to Hamiltonian PDEs and present a complete proof of the "KAM for PDEs" theorem. It will be an invaluable source of information for postgraduate mathematics and physics students and researchers.