- English
- ePUB (mobile friendly)
- Available on iOS & Android
Exact Methods for Nonlinear PDEs
About this book
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.
Frequently asked questions
- Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
- Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Information
Table of contents
- Cover Page
- Half-Title Page
- Series Page
- Title Page
- Copyright Page
- Contents
- Preface
- Some Notations and Remarks
- Author
- 1. Elementary Invariant Theory: Algebraic Equations and Ordinary Differential Equations
- 2. First-Order Partial Differential Equations
- 6. Methods of Functional Separation of Variables
- 7. Direct Method 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 by Solutions of Simpler Equations
- References for Chapter 12
- Index