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Exact Methods for Nonlinear PDEs
出版済み 3-5週間でお届けいたします。
Title: Exact Methods for Nonlinear PDEs Series: Advances in Applied Mathematics Author: Polyanin, Andrei D. Publisher: Taylor & Francis ISBN: 9781032710518 Cover: HARDCOVER Date: 2025年08月 こちらの商品は学校・法人様向け（機関契約）のオンラインブック版がございます。 オンラインブックの価格、納期につきましては弊社営業員または当ECサイトよりお問い合わせください。  DESCRIPTION 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. TABLE OF CONTENTS 1.Elementary Invariant Theory: Algebraic Equations and ODEs 2.First-Order Partial Differential Equations 3.Solution Methods for Functional Equations 4.Elementary Invariant Theory: Partial Differential Equations 5.Methods of Generalized Separation of Variables 6.Methods of Functional Separation of Variables 7.DirectMethod of Symmetry Reductions. Weak Symmetries 8.Classical Method of Symmetry Reductions 9.Differential Constraints Method 10.Transformations of Equations of Mathematical Physics 11.Using Simple Solutions to Construct Complex Solutions 12.Constructing Solutions of Complex Equations 最近チェックした商品
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