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
Download or read book Lie and Non Lie Symmetries written by and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation Since the end of the 19th century when the prominent Norwegian mathematician Sophus Lie created the theory of Lie algebras and Lie groups and developed the method of their applications for solving differential equations, his theory and method have continuously been the research focus of many well-known mathematicians and physicists. This book is devoted to recent development in Lie theory and its applications for solving physically and biologically motivated equations and models. The book contains the articles published in two Special Issue of the journal Symmetry, which are devoted to analysis and classification of Lie algebras, which are invariance algebras of real-word models; Lie and conditional symmetry classification problems of nonlinear PDEs; the application of symmetry-based methods for finding new exact solutions of nonlinear PDEs (especially reaction-diffusion equations) arising in applications; the application of the Lie method for solving nonlinear initial and boundary-value problems (especially those for modelling processes with diffusion, heat transfer, and chemotaxis).
Download or read book General Fractional Derivatives written by Xiao-Jun Yang and published by CRC Press. This book was released on 2019-05-10 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science. Features: Give some new results for fractional calculus of constant and variable orders. Discuss some new definitions for fractional calculus with respect to another function. Provide definitions for general fractional calculus of constant and variable orders. Report new results of general fractional calculus with respect to another function. Propose news special functions with respect to another function and their applications. Present new models for the anomalous relaxation and rheological behaviors. This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students. Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science.
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.
Download or read book Group Analysis of Differential Equations written by L. V. Ovsiannikov and published by Academic Press. This book was released on 2014-05-10 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations. This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the given differential equation with a known admitted group. The theory of differential invariants that is developed on an infinitesimal basis is elaborated in Chapter VII. The last chapter outlines the ways in which the methods of group analysis are used in special issues involving differential equations. This publication is a good source for students and specialists concerned with areas in which ordinary and partial differential equations play an important role.
Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer Nature. This book was released on 2020-10-15 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
Download or read book Symmetry Analysis of Differential Equations with Mathematica written by Gerd Baumann and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to explicitly use Mathematica so as to allow researchers and students to more easily compute and solve almost any kind of differential equation using Lie's theory. Previously time-consuming and cumbersome calculations are now much more easily and quickly performed using the Mathematica computer algebra software. The material in this book, and on the accompanying CD-ROM, will be of interest to a broad group of scientists, mathematicians and engineers involved in dealing with symmetry analysis of differential equations. Each section of the book starts with a theoretical discussion of the material, then shows the application in connection with Mathematica. The cross-platform CD-ROM contains Mathematica (version 3.0) notebooks which allow users to directly interact with the code presented within the book. In addition, the author's proprietary "MathLie" software is included, so users can readily learn to use this powerful tool in regard to performing algebraic computations.
Download or read book Separation of Variables and Exact Solutions to Nonlinear PDEs written by Andrei D. Polyanin and published by CRC Press. This book was released on 2021-09-19 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Separation of Variables and Exact Solutions to Nonlinear PDEs is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear partial differential equations (PDEs). It also presents the direct method of symmetry reductions and its more general version. In addition, the authors describe the differential constraint method, which generalizes many other exact methods. The presentation involves numerous examples of utilizing the methods to find exact solutions to specific nonlinear equations of mathematical physics. The equations of heat and mass transfer, wave theory, hydrodynamics, nonlinear optics, combustion theory, chemical technology, biology, and other disciplines are studied. Particular attention is paid to nonlinear equations of a reasonably general form that depend on one or several arbitrary functions. Such equations are the most difficult to analyze. Their exact solutions are of significant practical interest, as they are suitable to assess the accuracy of various approximate analytical and numerical methods. The book contains new material previously unpublished in monographs. It is intended for a broad audience of scientists, engineers, instructors, and students specializing in applied and computational mathematics, theoretical physics, mechanics, control theory, chemical engineering science, and other disciplines. Individual sections of the book and examples are suitable for lecture courses on partial differential equations, equations of mathematical physics, and methods of mathematical physics, for delivering special courses and for practical training.
Download or read book Introduction to Symmetry Analysis Paperback with CD ROM written by Brian Cantwell and published by Cambridge University Press. This book was released on 2002-09-23 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to symmetry analysis for graduate students in science, engineering and applied mathematics.
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.
Download or read book Games and Dynamics in Economics written by Ferenc Szidarovszky and published by Springer Nature. This book was released on 2020-04-11 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the latest advances in nonlinear dynamic modeling in economics and finance, mainly—but not solely—based on the description of strategic interaction by using concepts and methods from dynamic and evolutionary game theory. The respective chapters cover a range of theoretical issues and examples concerning how the qualitative theory of dynamical systems is used to analyze the local and global bifurcations that characterize complex behaviors observed in social systems where heterogeneous and boundedly rational economic agents interact. Nonlinear dynamical systems, represented by difference and differential and functional equations, are extensively used to simulate the behavior of time-evolving economic systems, also in the presence of time lags, discontinuities, and hysteresis phenomena. In addition, some theoretical issues and particular applications are discussed, as well. The contributions gathered here offer an up-to-date review of the latest research in this rapidly developing research area.
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.
Download or read book Elementary Lie Group Analysis and Ordinary Differential Equations written by Nailʹ Khaĭrullovich Ibragimov and published by John Wiley & Sons. This book was released on 1999-05-04 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lie's striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail. * This is the first modern text on ordinary differential equations where the basic integration methods are derived from Lie group theory * Includes a concise and self contained introduction to differential equations * Easy to follow and comprehensive introduction to Lie group analysis * The methods described in this book have many applications The author provides students and their teachers with a flexible text for undergraduate and postgraduate courses, spanning a variety of topics from the basic theory through to its many applications. The philosophy of Lie groups has become an essential part of the mathematical culture for anyone investigating mathematical models of physical, engineering and natural problems.
Download or read book Applications of Lie Groups to Differential Equations written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.
Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer. This book was released on 2016-12-10 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.Recently, the trend has been towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.“div>This is a large interdisciplinary and interrelated field, and the present volume is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
Download or read book Geometric Analysis of Nonlinear Partial Differential Equations written by Valentin Lychagin and published by MDPI. This book was released on 2021-09-03 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of twelve papers that reflect the state of the art of nonlinear differential equations in modern geometrical theory. It comprises miscellaneous topics of the local and nonlocal geometry of differential equations and the applications of the corresponding methods in hydrodynamics, symplectic geometry, optimal investment theory, etc. The contents will be useful for all the readers whose professional interests are related to nonlinear PDEs and differential geometry, both in theoretical and applied aspects.
Download or read book COMPUTATIONAL MODELS Volume I written by Shaidurov Vladimir Viktorovich and published by EOLSS Publications. This book was released on 2009-04-10 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Models is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. Modern Computational Mathematics arises in a wide variety of fields, including business, economics, engineering, finance, medicine and science. The Theme on Computational Models provides the essential aspects of Computational Mathematics emphasizing Basic Methods for Solving Equations; Numerical Analysis and Methods for Ordinary Differential Equations; Numerical Methods and Algorithms; Computational Methods and Algorithms; Numerical Models and Simulation. These two volumes are aimed at those seeking in-depth of advanced knowledge: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs.
