Symmetry analysis and exact solutions of equations of nonlinear mathematical physics

by V. I. Fushchich

Publisher: Kluwer in Dordrecht, London

Written in English
Published: Pages: 435 Downloads: 847
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Edition Notes

StatementW.I. Fushchich, W.M. Shtelen and N.I. Serov.
SeriesMathematics and its applications -- Vol.246
ContributionsShtelen", V. M., Serov, N. I.
The Physical Object
Paginationxxiv,435p. ;
Number of Pages435
ID Numbers
Open LibraryOL22618569M
ISBN 100792321464

Introduction to symmetry analysis / Brian J. Cantwell. p. cm. – (Cambridge texts in applied mathematics) Includes bibliographical references and index. ISBN – ISBN 1. Differential equations – Numerical solutions 2. Symmetry (Physics) I. Title. II. Series. QAC – dc21 ISBN 0 Add Equation/Solution Write/Publish Book. Information. Mathematical Sites Mathematical Books Errata in Handbooks Online Shops Publishers Journals Conferences Ask a Math Expert. Pastime. Math Humor and Jokes Math Puzzles & Games: Exact Solutions Methods Software For Authors Math Forums. Exact Solutions > Equation Index > Index of Named.   () Symmetry analysis and group-invariant solutions to inhomogeneous nonlinear diffusion equation. Communications in Nonlinear Science and Numerical Simulation , () Conditional Lie–Bäcklund symmetry, second-order differential constraint and direct reduction of diffusion by: 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.

() Symmetry analysis and exact solutions of some Ostrovsky equations. Theoretical and Mathematical Physics , () On a new method for finding generalized equivalence transformations for differential equations involving arbitrary by: The concept of approximate symmetry is introduced. The authors describe all nonlinearities F(u) with which the nonlinear wave equation Square Operator u+ lambda u 3 + epsilon F(u)=0 with a small parameter epsilon is approximately scale and conformally invariant. Some approximate solutions of wave equations in question are obtained using the approximate by: Kudryashov N. A., Seven common errors in finding exact solutions of nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simulation, ; Lectures on Linear Partial Differential Equations (MIT OpenCourseWare) by M.J. Hancock Lectures on Solution Methods for Nonlinear Mathematical Physics Equations by A.D. Polyanin.   Wang M, Zhou Y, Li Z: Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Phys. Lett. A , /(96) Article; Google ScholarCited by:

Symmetry methods for differential equations: a beginner’s guide / Peter E. Hydon. p. cm. – (Cambridge texts in applied mathematics) Includes bibliographical references and index. ISBN 1. Differential equations–Numerical solutions. 2. Symmetry. 3. Mathematical physics. I. Title. II. Series. QCD5H93 File Size: KB.   Description; Chapters; Supplementary; A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book — which aims to present new mathematical curricula based on symmetry .   A nice book to start with if you want to learn more is the introduction book (symmetry methods for differential equations) from Peter Hydon. Or if you are looking for algorithms that are systematically searching for symmetries, there are many papers from Cheb-terrab et al, who worked a lot on the ode solvers in Maple.   Take the field equations in vacuum, with no mass whatsoever. Then, try to find a stationary solution of the nonlinear field equations. One could image some kind of peculiar curvature of spacetime (for instance with spherical symmetry) in which this curvature is in fact the source of its own curvature.

Symmetry analysis and exact solutions of equations of nonlinear mathematical physics by V. I. Fushchich Download PDF EPUB FB2

Buy Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Mathematics and Its Applications) on FREE SHIPPING on qualified orders Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics (Mathematics and Its Applications): Fushchich, W.I., Shtelen, W.M., Serov, N.I.

Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics. Authors: Fushchich, W.I., Shtelen, W.M., Serov, N.I field equations is emphasized because their solutions can be used for constructing solutions of other field equations insofar as fields with any spin may be constructed from spin s = 1/2 fields.

A brief. Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics W. Fushchich, W. Shtelen, N. Serov (auth.) by spin or (spin s = 1/2) field equations is emphasized because their solutions can be used for constructing solutions of other field equations insofar as fields with any spin may be constructed from spin s = 1/2 fields.

About this book. Introduction. by spin or (spin s = 1/2) field equations is emphasized because their solutions can be used for constructing solutions of other field equations insofar as fields with any spin may be constructed from spin s = 1/2 fields. A brief account of the main ideas of the book is presented in the Introduction.

The book provides an overview of the current status of theoretical-algebraic methods in relation to linear and nonlinear multidimensional equations in mathematical and theoretical physics that are invariant with respect to the Poincare and Galilean groups and the wider Lie groups.

Particular attention is given to the construction, in explicit form, of wide classes of accurate solutions to. Abstract: The authors give a detailed information about symmetry (Lie, non-Lie, conditional) of nonlinear PDEs for spinor, vector and scalar fields; using advanced methods of group-theoretical, symmetry analysis construct wide families of classical solutions of the nonlinear Dirac, Yang-Mills, Maxwell-Dirac, Dirac-d'Alembert, d'Alembert-Hamilton equations; expound a new symmetry Cited by: Part of the CRM Series in Mathematical Physics book series (CRM) The purpose of these lectures is to show how the method of symmetry reduction can be used to obtain certain classes of exact analytic solutions of systems of partial differential equations.

We use the words “symmetry reduction” in a rather broad by: Nonlinear determining equations for potentials are solved using reductions to Weierstrass, Painlevé, and Riccati forms. Algebraic properties of higher order symmetry operators are analyzed. Combinations of higher and conditional symmetries are used to generate families of exact solutions of linear and nonlinear Symmetry analysis and exact solutions of equations of nonlinear mathematical physics book by: Full text of "Symmetries and Exact Solutions of Nonlinear Dirac Equations" See other formats.

Finding analytic exact solutions to non-linear heat conduction (diffusion) equations arising from variable thermal conductivity is a challenging task. Recently Pakdemirli and Sahin [11] have used symmetry methods in an attempt to obtain some similarity solutions of a non-linear fin equation arising from temperature dependent thermal Cited by: Symmetry Reductions and Exact Solutions for Nonlinear Diffusion Equations Article (PDF Available) in International Journal of Modern Physics A.

Abstract. The authors give a detailed information about symmetry (Lie, non-Lie, conditional) of nonlinear PDEs for spinor, vector and scalar fields; using advanced methods of group-theoretical, symmetry analysis construct wide families of classical solutions of the nonlinear Dirac, Yang-Mills, Maxwell-Dirac, Dirac-d'Alembert, d'Alembert-Hamilton equations; expound a new symmetry Author: Wilhelm Fushchych and Renat Zhdanov.

Abstract. Using the invariance group properties of the governing system of partial differential equations (PDEs), admitting Lie group of point transformations with commuting infinitesimal generators, we obtain exact solutions to the system of PDEs describing one-dimensional unsteady planar and cylindrically symmetric motions in magnetogasdynamics Cited by: Recent Advances in Symmetry Analysis and Exact Solutions in Nonlinear Mathematical Physics Maria Bruzón, 1 Chaudry M.

Khalique, 2 Maria L. Gandarias, 1 Rita Traciná, 3 and Mariano Torrisi 3 1 University of Cádiz, Cádiz, SpainAuthor: Maria Bruzón, Chaudry M.

Khalique, Maria L. Gandarias, Rita Traciná, Mariano Torrisi. and construction of exact solutions of nonlinear differential equations. Moreover, the latest trends in symmetry analysis, such as conditional symmetry, potential symmetries, discrete symmetries and differential geometry approach to symmetry analysis were represented efficiently.

In addition, important branches of symmetry analysis such as repre-File Size: 1MB. We have obtained the infinitesimal generators, commutator table of Lie algebra and symmetry group.

In addition to that, optimal system of one-dimensional subalgebras up to conjugacy is derived and used to construct distinct exact solutions. These solutions describe the dynamics of nonlinear waves in isothermal multicomponent magnetized by: 1.

Many systematic methods are usually employed to study the nonlinear equations: these include the generalized symmetry method, the Painlevé analysis, the inverse scattering method, the Bäcklund transformation method, the conservation law method, the Cole-Hopf transformation, and the Hirota bilinear method.

Abstract The authors give a detailed information about symmetry (Lie, non-Lie, conditional) of nonlinear PDEs for spinor, vector and scalar fields; using advanced methods of group-theoretical, symmetry analysis construct wide families of classical solutions of the nonlinear Dirac, Yang-Mills, Maxwell-Dirac, Dirac-d'Alembert, d'Alembert-Hamilton equations; expound a new symmetry.

We derive some exact solutions of a nonlinear diffusion-convection-reaction equation which models biological, chemical and physical phenomena. The Lie symmetry classification approach is employed to specify the model parameters and then the symmetries of resulting submodels are utilized for construction of exact by: 2.

Book description. Symmetry is the key to solving differential equations. There are many well-known techniques for obtaining exact solutions, but most of them are special cases of a few powerful symmetry methods. Furthermore, these methods can be applied to differential equations of an unfamiliar type; they do not rely on special 'tricks'.Cited by: Symmetry Analysis of Differential Equations: An Introduction is an ideal textbook for upper-undergraduate and graduate-level courses in symmetry methods and applied mathematics.

The book is also a useful reference for professionals in science, physics, and engineering, as well as anyone wishing to learn about the use of symmetry methods in solving differential equations. A self-contained introduction to the methods and techniques of symmetry analysis used to solve ODEs and PDEs Symmetry Analysis of Differential Equations: An Introduction presents an accessible approach to the uses of symmetry methods in solving both ordinary differential equations (ODEs) and partial differential equations (PDEs).

Providing comprehensive coverage, the book. The author of over 30 journal articles, his research interests include the construction of exact solutions of PDEs; symmetry analysis of nonlinear PDEs; and solutions to physically important equations, such as nonlinear heat equations and governing equations modeling of granular materials and nonlinear by: 2.

Symmetry in Nonlinear Mathematical PhysicsV.2, – Quantum Mechanics in Noninertial Reference Frames and Representations of the Euclidean Line Group W.H. KLINK 1 Department of Physics and Astronomy, Department of Mathematics, University of Iowa, Iowa City, IAUSA FAX: () E-mail: [email protected] AbstractFile Size: 1MB.

Symmetry analysis and exact solutions of equations of nonlinear mathematical physics. Dordrecht ; Boston: Kluwer Academic Publishers, © (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: V I Fushchich; V M Shtelenʹ; N I Serov.

Get this from a library. Symmetry analysis and exact solutions of equations of nonlinear mathematical physics. [Vil'gel'm I Fuščič; N I Serov; V M Štelen']. families of their exact solutions, a majority of which are new and might be of considerable interest for applications.

Plan. Introduction 2. Conformally-invariant ansatzes for an arbitrary vector field 3. Exact solutions of the Yang-Mills equations 4. Conditional symmetry and new solutions of the Yang-Mills equations 5.

Lie symmetry analysis is one of the most powerful and systematic methods, which plays a very important role in finding an exact solution of such nonlinear coupled evolution equations.

For the theory of Lie group analysis and its applications to differential equations we. In this paper, the Lie symmetry analysis method is employed to investigate the Lie point symmetries and the one-parameter transformation groups of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system.

By using Ibragimov’s method, the optimal system of one-dimensional subalgebras of this system is constructed. Truncated Painlevé analysis is used for deriving Cited by: This paper is based on finding the exact solutions for Burger’s equation, Zakharov-Kuznetsov (ZK) equation and Kortewegde vries (KdV) equation by utilizing exponential function method that depends on the series of exponential functions.

The exponential function method utilizes the homogeneous balancing principle to find the solutions of nonlinear : Shumaila Javeed, Khurram Saleem Alimgeer, Sidra Nawaz, Asif Waheed, Muhammad Suleman, Dumitru Balean. as in Kerr law nonlinear medium. In mathematical physics, the generic equations (1) and (2) fall under the category of nonlinear evolution equations (NLEEs).

3. SYMMETRY ANALYSIS AND SYMMETRY REDUCTIONS The investigation of exact solutions to NLEEs is a quite important task in the nonlinear science.Broadly, my research lies in nonlinear differential equations, symmetry analysis, integrability and solitons, and mathematical physics.

My interests in nonlinear differential equations center on applications of symmetry analysis and conservation laws to the study of PDEs, particularly nonlinear wave equations and soliton equations, as well as ODEs connected with exact solutions .Using the nonclassical symmetry of nonlinear reaction–diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen–Cahn–Hilliard equation.

This models a phase field that gives a phenomenological description of a two-phase system near critical temperature.