Exact Solutions And Invariant Subspaces Of Nonlinear Partial Differential Equations In Mechanics And Physics
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Exact Solutions And Invariant Subspaces Of Nonlinear Partial Differential Equations In Mechanics And Physics
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Author : Victor A. Galaktionov
language : en
Publisher: CRC Press
Release Date : 2006-11-02
Exact Solutions And Invariant Subspaces Of Nonlinear Partial Differential Equations In Mechanics And Physics written by Victor A. Galaktionov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-02 with Mathematics categories.
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties. This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.
Symmetry And Exact Solutions Of Nonlinear Mathematical Physics Equations
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Author : Gangwei Wang
language : en
Publisher: Frontiers Media SA
Release Date : 2024-08-13
Symmetry And Exact Solutions Of Nonlinear Mathematical Physics Equations written by Gangwei Wang and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-13 with Science categories.
Nonlinear problems, originating from applied science that is closely related to practices, contain rich and extensive content. It makes the corresponding nonlinear models also complex and diverse. Due to the intricacy and contingency of nonlinear problems, unified mathematical methods still remain far and few between. In this regard, the comprehensive use of symmetric methods, along with other mathematical methods, becomes an effective option to solve nonlinear problems.
Separation Of Variables And Exact Solutions To Nonlinear Pdes
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2021-09-19
Separation Of Variables And Exact Solutions To Nonlinear Pdes written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-19 with Mathematics categories.
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.
Exact Methods For Nonlinear Pdes
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2025-08-13
Exact Methods For Nonlinear Pdes written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-13 with Mathematics categories.
Exact Methods for Nonlinear PDEs describes effective analytical methods for finding exact solutions to nonlinear differential equations of mathematical physics and other partial differential equations and also demonstrates the practical applications of these methods. It covers the methods of generalized separation of variables, methods of functional separation of variables, the classical method of symmetry reductions, the direct method of symmetry reductions, the method of weak symmetry reductions, and the method of differential constraints. The book presents several simple methods for finding exact solutions to nonlinear partial differential equations (PDEs). These methods do not require specialized knowledge and aim to minimize intermediate calculations. For the first time, it discusses the application of nonrigorous, intuitive reasoning in deriving exact solutions to nonlinear PDEs. Each section provides numerous examples, problems, and exercises to help readers develop practical skills in applying the methods. The material is illustrated with equations of mass and heat transfer, hydrodynamics, wave theory, nonlinear optics, and other nonlinear equations of mathematical physics. The key points that distinguish this book from others in the field include: • it presents many methods in a simpler and more visual format; • it describes a number of simple methods for constructing exact solutions to nonlinear PDEs and delay PDEs; • it emphasizes and details the practical use of non-rigorous reasoning to derive exact solutions for nonlinear PDEs. The book is intended for a diverse audience, including researchers, university professors, engineers, postgraduates, and students specializing in applied mathematics, theoretical physics, and engineering sciences.
Mathematical Methods In Engineering
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Author : Kenan Taş
language : en
Publisher: Springer
Release Date : 2018-08-21
Mathematical Methods In Engineering written by Kenan Taş and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-21 with Technology & Engineering categories.
This book collects chapters dealing with some of the theoretical aspects needed to properly discuss the dynamics of complex engineering systems. The book illustrates advanced theoretical development and new techniques designed to better solve problems within the nonlinear dynamical systems. Topics covered in this volume include advances on fixed point results on partial metric spaces, localization of the spectral expansions associated with the partial differential operators, irregularity in graphs and inverse problems, Hyers-Ulam and Hyers-Ulam-Rassias stability for integro-differential equations, fixed point results for mixed multivalued mappings of Feng-Liu type on Mb-metric spaces, and the limit q-Bernstein operators, analytical investigation on the fractional diffusion absorption equation.
Handbook Of Exact Solutions To Mathematical Equations
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2024-08-26
Handbook Of Exact Solutions To Mathematical Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-26 with Mathematics categories.
This reference book describes the exact solutions of the following types of mathematical equations: ● Algebraic and Transcendental Equations ● Ordinary Differential Equations ● Systems of Ordinary Differential Equations ● First-Order Partial Differential Equations ● Linear Equations and Problems of Mathematical Physics ● Nonlinear Equations of Mathematical Physics ● Systems of Partial Differential Equations ● Integral Equations ● Difference and Functional Equations ● Ordinary Functional Differential Equations ● Partial Functional Differential Equations The book delves into equations that find practical applications in a wide array of natural and engineering sciences, including the theory of heat and mass transfer, wave theory, hydrodynamics, gas dynamics, combustion theory, elasticity theory, general mechanics, theoretical physics, nonlinear optics, biology, chemical engineering sciences, ecology, and more. Most of these equations are of a reasonably general form and dependent on free parameters or arbitrary functions. The Handbook of Exact Solutions to Mathematical Equations generally has no analogs in world literature and contains a vast amount of new material. The exact solutions given in the book, being rigorous mathematical standards, can be used as test problems to assess the accuracy and verify the adequacy of various numerical and approximate analytical methods for solving mathematical equations, as well as to check and compare the effectiveness of exact analytical methods.
Lie And Non Lie Symmetries Theory And Applications For Solving Nonlinear Models
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Author : Roman M. Cherniha
language : en
Publisher: MDPI
Release Date : 2018-07-06
Lie And Non Lie Symmetries Theory And Applications For Solving Nonlinear Models written by Roman M. Cherniha and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-06 with Mathematics categories.
This book is a printed edition of the Special Issue "Lie Theory and Its Applications" that was published in Symmetry
Nonlinear Reaction Diffusion Systems
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Author : Roman Cherniha
language : en
Publisher: Springer
Release Date : 2017-09-18
Nonlinear Reaction Diffusion Systems written by Roman Cherniha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-18 with Mathematics categories.
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.
Algebraic Approaches To Partial Differential Equations
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Author : Xiaoping Xu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-23
Algebraic Approaches To Partial Differential Equations written by Xiaoping Xu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-23 with Mathematics categories.
This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation, the KP equation, the nonlinear Schrodinger equation, the Davey and Stewartson equations, the Boussinesq equations in geophysics, the Navier-Stokes equations and the boundary layer problems. In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions, symmetry transformations, linearization techniques and special functions. The book is self-contained and requires only a minimal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, the sciences and engineering. Readers may find the exact solutions and mathematical skills needed in their own research.
Advanced Computing In Industrial Mathematics
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Author : Krassimir Georgiev
language : en
Publisher: Springer
Release Date : 2018-09-27
Advanced Computing In Industrial Mathematics written by Krassimir Georgiev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-27 with Technology & Engineering categories.
This book gathers the peer-reviewed proceedings of the 12th Annual Meeting of the Bulgarian Section of the Society for Industrial and Applied Mathematics, BGSIAM’17, held in Sofia, Bulgaria, in December 2017. The general theme of BGSIAM’17 was industrial and applied mathematics, with a particular focus on: high-performance computing, numerical methods and algorithms, analysis of partial differential equations and their applications, mathematical biology, control and uncertain systems, stochastic models, molecular dynamics, neural networks, genetic algorithms, metaheuristics for optimization problems, generalized nets, and Big Data.