Nonlinear Symmetries And Nonlinear Equations

Author : G. Gaeta
Publisher : Springer Science & Business Media
ISBN 13 : 9401110182
Total Pages : 275 pages
Book Rating : 4.81/5 ( download)

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Download or read book Nonlinear Symmetries and Nonlinear Equations written by G. Gaeta and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of (nonlinear) dift"erential equations was S. Lie's motivation when he created what is now known as Lie groups and Lie algebras; nevertheless, although Lie group and algebra theory flourished and was applied to a number of dift"erent physical situations -up to the point that a lot, if not most, of current fun damental elementary particles physics is actually (physical interpretation of) group theory -the application of symmetry methods to dift"erential equations remained a sleeping beauty for many, many years. The main reason for this lies probably in a fact that is quite clear to any beginner in the field. Namely, the formidable comple:rity ofthe (algebraic, not numerical!) computations involved in Lie method. I think this does not account completely for this oblivion: in other fields of Physics very hard analytical computations have been worked through; anyway, one easily understands that systems of dOlens of coupled PDEs do not seem very attractive, nor a very practical computational tool.

Author : Giampaolo Cicogna
Publisher : Springer Science & Business Media
ISBN 13 : 354048874X
Total Pages : 218 pages
Book Rating : 4.43/5 ( download)

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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.

Author : Roman Cherniha
Publisher : CRC Press
ISBN 13 : 1351650874
Total Pages : 244 pages
Book Rating : 4.78/5 ( download)

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Download or read book Nonlinear Reaction-Diffusion-Convection Equations written by Roman Cherniha and published by CRC Press. This book was released on 2017-11-02 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that symmetry-based methods are very powerful tools for investigating nonlinear partial differential equations (PDEs), notably for their reduction to those of lower dimensionality (e.g. to ODEs) and constructing exact solutions. This book is devoted to (1) search Lie and conditional (non-classical) symmetries of nonlinear RDC equations, (2) constructing exact solutions using the symmetries obtained, and (3) their applications for solving some biologically and physically motivated problems. The book summarises the results derived by the authors during the last 10 years and those obtained by some other authors.

Author : Klaus Mainzer
Publisher : World Scientific
ISBN 13 : 9812561927
Total Pages : 448 pages
Book Rating : 4.23/5 ( download)

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Download or read book Symmetry and Complexity written by Klaus Mainzer and published by World Scientific. This book was released on 2005 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cosmic evolution leads from symmetry to complexity by symmetry breaking and phase transitions. The emergence of new order and structure in nature and society is explained by physical, chemical, biological, social and economic self-organization, according to the laws of nonlinear dynamics. All these dynamical systems are considered computational systems processing information and entropy. Are symmetry and complexity only useful models of science or are they universals of reality? Symmetry and Complexity discusses the fascinating insights gained from natural, social and computer sciences, philosophy and the arts. With many diagrams and pictures, this book illustrates the spirit and beauty of nonlinear science. In the complex world of globalization, it strongly argues for unity in diversity.

Author : Muthuswamy Lakshmanan
Publisher : Springer Science & Business Media
ISBN 13 : 3642760465
Total Pages : 219 pages
Book Rating : 4.64/5 ( download)

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Download or read book Symmetries and Singularity Structures written by Muthuswamy Lakshmanan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Workshop, Bharathidasan University, Tiruchirapalli, India, November 29 - December 2, 1989

Author : Roman Cherniha
Publisher : Springer
ISBN 13 : 3319654675
Total Pages : 160 pages
Book Rating : 4.76/5 ( download)

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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 160 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.

Author : D Levi
Publisher : World Scientific
ISBN 13 : 9813201533
Total Pages : 473 pages
Book Rating : 4.38/5 ( download)

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Download or read book Symmetries And Nonlinear Phenomena - Proceedings Of The International School On Applied Mathematics written by D Levi and published by World Scientific. This book was released on 1988-12-01 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from Sophus Lie, the invariance of a differential equation under its continuous group of symmetries has become a major tool for solving ordinary and partial differential equations, in particular, nonlinear ones. The proceedings focus on the application of these techniques to nonlinear partial differential equations. The state of the art in this field is presented clearly in a series of comprehensive lectures. Several lectures on applications point out the physical importance of such methods.

Author : Laura Menini
Publisher : Springer Science & Business Media
ISBN 13 : 0857296124
Total Pages : 344 pages
Book Rating : 4.22/5 ( download)

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Download or read book Symmetries and Semi-invariants in the Analysis of Nonlinear Systems written by Laura Menini and published by Springer Science & Business Media. This book was released on 2011-05-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book details the analysis of continuous- and discrete-time dynamical systems described by differential and difference equations respectively. Differential geometry provides the tools for this, such as first-integrals or orbital symmetries, together with normal forms of vector fields and of maps. A crucial point of the analysis is linearization by state immersion. The theory is developed for general nonlinear systems and specialized for the class of Hamiltonian systems. By using the strong geometric structure of Hamiltonian systems, the results proposed are stated in a different, less complex and more easily comprehensible manner. They are applied to physically motivated systems, to demonstrate how much insight into known properties is gained using these techniques. Various control systems applications of the techniques are characterized including: computation of the flow of nonlinear systems; computation of semi-invariants; computation of Lyapunov functions for stability analysis and observer design.

Author : Roman M. Cherniha
Publisher : MDPI
ISBN 13 : 3038425265
Total Pages : 427 pages
Book Rating : 4.67/5 ( download)

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Download or read book Lie and non-Lie Symmetries: Theory and Applications for Solving Nonlinear Models written by Roman M. Cherniha and published by MDPI. This book was released on 2018-07-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Lie Theory and Its Applications" that was published in Symmetry

Author : Brian J. Cantwell
Publisher : Cambridge University Press
ISBN 13 : 9781139431712
Total Pages : 670 pages
Book Rating : 4.14/5 ( download)

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Download or read book Introduction to Symmetry Analysis written by Brian J. Cantwell and published by Cambridge University Press. This book was released on 2002-09-23 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry analysis based on Lie group theory is the most important method for solving nonlinear problems aside from numerical computation. The method can be used to find the symmetries of almost any system of differential equations and the knowledge of these symmetries can be used to reduce the complexity of physical problems governed by the equations. This is a broad, self-contained, introduction to the basics of symmetry analysis for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. MathReader 4.0 is included to let the user read the sample notebooks and follow the procedure used to find symmetries.