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Dynamics Symmetry And Pdes
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Book Synopsis Dynamical Symmetry by : Carl Wulfman
Download or read book Dynamical Symmetry written by Carl Wulfman and published by World Scientific. This book was released on 2011 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whenever systems are governed by continuous chains of causes and effects, their behavior exhibits the consequences of dynamical symmetries, many of them far from obvious. Dynamical Symmetry introduces the reader to Sophus Lie's discoveries of the connections between differential equations and continuous groups that underlie this observation. It develops and applies the mathematical relations between dynamics and geometry that result. Systematic methods for uncovering dynamical symmetries are described, and put to use. Much material in the book is new and some has only recently appeared in research journals. Though Lie groups play a key role in elementary particle physics, their connection with differential equations is more often exploited in applied mathematics and engineering. Dynamical Symmetry bridges this gap in a novel manner designed to help readers establish new connections in their own areas of interest. Emphasis is placed on applications to physics and chemistry. Applications to many of the other sciences illustrate both general principles and the ubiquitousness of dynamical symmetries.
Book Synopsis Dynamics of Partial Differential Equations by : C. Eugene Wayne
Download or read book Dynamics of Partial Differential Equations written by C. Eugene Wayne and published by Springer. This book was released on 2015-08-08 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equations with very different physical origins and mathematical properties.
Book Synopsis Applications of Symmetry Methods to Partial Differential Equations by : George W. Bluman
Download or read book Applications of Symmetry Methods to Partial Differential Equations written by George W. Bluman and published by Springer Science & Business Media. This book was released on 2009-10-30 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Bäcklund symmetries, contact transformations, adjoint symmetries, Nöther's Theorem, mappings with some modification, potential symmetries, nonlocal symmetries, nonlocal mappings, and non-classical method. Of use to graduate students and researchers in mathematics and physics.
Download or read book Dynamics, Symmetry and PDEs written by and published by . This book was released on 1997 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: Patterns appear in physical, chemical, and biological systems and are characteristically striking and reproducible. Consequently, scientists and mathematicians have developed theories to explain the origins of these patterns. There are several approaches to the study of pattern; ours is based on symmetry and bifurcation. We have investigated both the theory and application of symmetric dynamical systems and its relation to pattern formation. In this work, pattern is identified with invariance under some of the underlying symmetries. In bounded domains, we have investigated bifurcations to spiral waves. We have also investigated chaotic dynamics where the pattern appears as symmetry on average. In a separate direction, we have considered pattern formation in unbounded domains. Our theoretical investigations have included the bifurcation and meandering of spirals and the Ginzburg-Landau theory of spatially extended systems - with application to spatially aperiodic solutions in spatially extended systems. Finally, part of our effort has been devoted to studying the dynamics present in (ordinary) differential equations with symmetry. For example, we have studied stable ergodicity of chaotic attractors in problems with continuous symmetry, and the existence, stability and bifurcations of robust heteroclinic cycles. Some of these ideas are relevant to intermittent magnetic dynamos in rotating Rayleigh-Benard convection.
Book Synopsis Symmetry and Perturbation Theory in Nonlinear Dynamics by : Giampaolo Cicogna
Download or read book Symmetry and Perturbation Theory in Nonlinear Dynamics written by Giampaolo Cicogna and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: has been in the of a Symmetry major ingredient development quantum perturba tion and it is a basic of the of theory, ingredient theory integrable (Hamiltonian and of the the use in context of non Hamiltonian) systems; yet, symmetry gen eral is rather recent. From the of view of nonlinear perturbation theory point the use of has become dynamics, widespread only through equivariant symmetry bifurcation in this attention has been confined to linear even theory; case, mostly symmetries. in recent the and of methods for dif Also, theory practice symmetry years ferential has become and has been to a equations increasingly popular applied of the of the book Olver This by variety problems (following appearance [2621). with is and deals of nature theory deeply geometrical symmetries general (pro vided that described i.e. in this context there is are vector no they by fields), to limit attention to linear reason symmetries. In this look the basic tools of i.e. normal book we at perturbation theory, introduced Poincar6 about and their inter a forms (first by century ago) study action with with no limitation to linear ones. We focus on the most symmetries, basic fixed the and i.e. a setting, systems having point (at origin) perturbative around thus is local.
Book Synopsis Differential Equations by : Hans Stephani
Download or read book Differential Equations written by Hans Stephani and published by Cambridge University Press. This book was released on 1989 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the theory and application of the solution to differential equations using symmetries, a technique of great value in mathematics and the physical sciences. It will apply to graduate students in physics, applied mathematics, and engineering.
Book Synopsis Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations by : Messoud Efendiev
Download or read book Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations written by Messoud Efendiev and published by Springer. This book was released on 2018-10-17 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.
Book Synopsis Dynamical Symmetry by : Carl E Wulfman
Download or read book Dynamical Symmetry written by Carl E Wulfman and published by World Scientific. This book was released on 2010-12-15 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whenever systems are governed by continuous chains of causes and effects, their behavior exhibits the consequences of dynamical symmetries, many of them far from obvious. Dynamical Symmetry introduces the reader to Sophus Lie's discoveries of the connections between differential equations and continuous groups that underlie this observation. It develops and applies the mathematical relations between dynamics and geometry that result. Systematic methods for uncovering dynamical symmetries are described, and put to use. Much material in the book is new and some has only recently appeared in research journals.Though Lie groups play a key role in elementary particle physics, their connection with differential equations is more often exploited in applied mathematics and engineering. Dynamical Symmetry bridges this gap in a novel manner designed to help readers establish new connections in their own areas of interest. Emphasis is placed on applications to physics and chemistry. Applications to many of the other sciences illustrate both general principles and the ubiquitousness of dynamical symmetries.
Book Synopsis Symmetries and Applications of Differential Equations by : Albert C. J. Luo
Download or read book Symmetries and Applications of Differential Equations written by Albert C. J. Luo and published by Springer Nature. This book was released on 2021-12-14 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about Lie group analysis of differential equations for physical and engineering problems. The topics include: -- Approximate symmetry in nonlinear physical problems -- Complex methods for Lie symmetry analysis -- Lie group classification, Symmetry analysis, and conservation laws -- Conservative difference schemes -- Hamiltonian structure and conservation laws of three-dimensional linear elasticity -- Involutive systems of partial differential equations This collection of works is written in memory of Professor Nail H. Ibragimov (1939–2018). It could be used as a reference book in differential equations in mathematics, mechanical, and electrical engineering.
Book Synopsis Dynamics and Symmetry by : Mike Field
Download or read book Dynamics and Symmetry written by Mike Field and published by World Scientific. This book was released on 2007 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the first systematic exposition of the global and local theory of dynamics equivariant with respect to a (compact) Lie group. Aside from general genericity and normal form theorems on equivariant bifurcation, it describes many general families of examples of equivariant bifurcation and includes a number of novel geometric techniques, in particular, equivariant transversality. This important book forms a theoretical basis of future work on equivariant reversible and Hamiltonian systems.This book also provides a general and comprehensive introduction to codimension one equivariant bifurcation theory. In particular, it includes the bifurcation theory developed with Roger Richardson on subgroups of reflection groups and the Maximal Isotropy Subgroup Conjecture. A number of general results are also given on the global theory. Introductory material on groups, representations and G-manifolds are covered in the first three chapters of the book. In addition, a self-contained introduction of equivariant transversality is given, including necessary results on stratifications as well as results on equivariant jet transversality developed by Edward Bierstone.
Book Synopsis Symmetry Methods for Differential Equations by : Peter Ellsworth Hydon
Download or read book Symmetry Methods for Differential Equations written by Peter Ellsworth Hydon and published by Cambridge University Press. This book was released on 2000-01-28 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a straightforward introduction to the subject of symmetry methods for solving differential equations, and is aimed at applied mathematicians, physicists, and engineers. The presentation is informal, using many worked examples to illustrate the main symmetry methods. It is written at a level suitable for postgraduates and advanced undergraduates, and is designed to enable the reader to master the main techniques quickly and easily.The book contains some methods that have not previously appeared in a text. These include methods for obtaining discrete symmetries and integrating factors.
Book Synopsis Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks by : Dmitry Pelinovsky
Download or read book Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks written by Dmitry Pelinovsky and published by MDPI. This book was released on 2019-10-30 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Special Issue focuses on recent progress in a new area of mathematical physics and applied analysis, namely, on nonlinear partial differential equations on metric graphs and branched networks. Graphs represent a system of edges connected at one or more branching points (vertices). The connection rule determines the graph topology. When the edges can be assigned a length and the wave functions on the edges are defined in metric spaces, the graph is called a metric graph. Evolution equations on metric graphs have attracted much attention as effective tools for the modeling of particle and wave dynamics in branched structures and networks. Since branched structures and networks appear in different areas of contemporary physics with many applications in electronics, biology, material science, and nanotechnology, the development of effective modeling tools is important for the many practical problems arising in these areas. The list of important problems includes searches for standing waves, exploring of their properties (e.g., stability and asymptotic behavior), and scattering dynamics. This Special Issue is a representative sample of the works devoted to the solutions of these and other problems.
Book Synopsis Nonlinear Reaction-Diffusion Systems by : Roman Cherniha
Download or read book Nonlinear Reaction-Diffusion Systems written by Roman Cherniha and published by Springer. This book was released on 2017-09-18 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception, parts of the book can also be used in master’s level mathematical biology courses.
Book Synopsis Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation by : Ovidiu Costin
Download or read book Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation written by Ovidiu Costin and published by Springer Science & Business Media. This book was released on 2011-04-30 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of a one-week international conference centered on asymptotic analysis and its applications. They contain major contributions dealing with - mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, - local dynamics: parabolic systems, small denominator questions, - new aspects in mould calculus, with related combinatorial Hopf algebras and application to multizeta values, - a new family of resurgent functions related to knot theory.
Book Synopsis Nonlinear PDE's, Dynamics and Continuum Physics by : J. L. Bona
Download or read book Nonlinear PDE's, Dynamics and Continuum Physics written by J. L. Bona and published by American Mathematical Soc.. This book was released on 2000 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the refereed proceedings of the conference on Nonlinear Partial Differential Equations, Dynamics and Continuum Physics which was held at Mount Holyoke College in Massachusetts, from July 19th to July 23rd, 1998. Models examined derive from a wide range of applications, including elasticity, thermoviscoelasticity, granular media, fluid dynamics, gas dynamics and conservation laws. Mathematical topics include existence theory and stability/instability of traveling waves, asymptotic behavior of solutions to nonlinear wave equations, effects of dissipation, mechanisms of blow-up, well-posedness and regularity, and fractal solutions. The text will be of interest to graduate students and researchers working in nonlinear partial differential equations and applied mathematics.
Book Synopsis Physics and Partial Differential Equations by : Tatsien Li
Download or read book Physics and Partial Differential Equations written by Tatsien Li and published by SIAM. This book was released on 2013-08-14 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now available in English for the first time, Physics and Partial Differential Equations, Volume I bridges physics and applied mathematics in a manner that is easily accessible to readers with an undergraduate-level background in these disciplines. Readers who are more familiar with mathematics than physics will discover the connection between various physical and mechanical disciplines and their related mathematical models, which are described by partial differential equations (PDEs). The authors establish the fundamental equations for fields such as electrodynamics; fluid dynamics, magnetohydrodynamics, and reacting fluid dynamics; elastic, thermoelastic, and viscoelastic mechanics; the kinetic theory of gases; special relativity; and quantum mechanics. Readers who are more familiar with physics than mathematics will benefit from in-depth explanations of how PDEs work as effective mathematical tools to more clearly express and present the basic concepts of physics. The book describes the mathematical structures and features of these PDEs, including the types and basic characteristics of the equations, the behavior of solutions, and some commonly used approaches to solving PDEs. Each chapter can be read independently and includes exercises and references.
Book Synopsis Dynamics, Bifurcation and Symmetry by : Pascal Chossat
Download or read book Dynamics, Bifurcation and Symmetry written by Pascal Chossat and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects contributions to the conference" Dynamics, Bifurcation and Symmetry, new trends and new tools", which was held at the Institut d'Etudes Sci entifiques de Cargese (France), September 3-9, 1993. The first aim of this conference was to gather and summarize the work of the European Bifurcation Theory Group after two years of existence (the EBTG links european laboratories in five countries via an EC grant). Thanks to a NATO ARW grant, the conference developed into an international meeting on bifurcation theory and dynamical systems, with the partic ipation of leading specialists not only from Europe but also from overseas countries (Canada, USA, South America). It was a great satisfaction to notice the active, and quite enthusiastic participation of many young scientists. This is reflected in the present book for which many contributors are PhD students or post-doc researchers. Although several "big" themes (bifurcation with symmetry, low dimensional dynam ics, dynamics in EDP's, applications, . . . ) are present in these proceedings, we have divided the book into corresponding parts. In fact these themes overlap in most contributions, which seems to reflect a general tendancy in nonlinear science. I am very pleased to thank for their support the NATO International Exchange Scientific Program as well as the EEC Science Program, which made possible the suc cess of this conference.
