This book presents developments in the geometric approach to nonlinear partial differential equations (PDEs). The expositions discuss the main features of the approach, and the theory of symmetries and the conservation laws based on it. The book combines rigorous mathematics with concrete examples. Nontraditional topics, such as the theory of nonlocal symmetries and cohomological theory of conservation laws, are also included. The volume is largely self-contained and includes detailed motivations, extensive examples and exercises, and careful proofs of all results. Readers interested in learning the basics of applications of symmetry methods to differential equations of mathematical physics will find the text useful. Experts will also find it useful as it gathers many results previously only available in journals.
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Editorial Reviews
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A valuable feature is that provides an overview of a number of results that originally appeared in Russian journals and are often difficult to track down. -- Mathematical Reviews
Rigorous mathematics and concrete examples illustrate the geometric approach to the study of nonlinear PDEs. --American Mathematical Monthly
Rigorous mathematics and concrete examples illustrate the geometric approach to the study of nonlinear PDEs. --American Mathematical Monthly
Language Notes
Text: English (translation)
Original Language: Russian
Original Language: Russian
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
5
books
cite this book:
- Smooth Manifolds and Observables by Jet Nestruev in Back Matter
- New Trends in Integrability and Partial Solvability (NATO Science Series II: Mathematics, Physics and Chemistry) by A.B. Shabat on page 215
- Geometric Approaches to Differential Equations (Australian Mathematical Society Lecture Series) by Peter J. Vassiliou on page 14
- Liapunov Functions and Stability in Control Theory (Communications and Control Engineering) by Andrea Bacciotti in Back Matter
- Noncommutative Structures in Mathematics and Physics (NATO Science Series II: Mathematics, Physics and Chemistry, Volume 22) by S. Duplij on page 390
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