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Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications, Series Number 101) - Hardcover
Synopsis
Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology).
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Book Description
Explains how to solve highly non-trivial nonlinear partial and ordinary differential equations using methods from contact and symplectic geometry. Combining the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia, it contains applications to problems ranging from Lie's classification problem to analysis of laser beams.
About the Author
Alexei Kushner is a Professor and Dean of the Department of Mathematics and Computer Science, and a Senior Researcher at the Russian Academy of Sciences.
Valentin Lychagin is a Professor at the Institute of Mathematics and Statistics, Tromsø University, and a Senior Researcher at the Institute for Theoretical and Experimental Physics in Moscow.
Vladimir Rubtsov is a Professor at the Département de Mathématiques, Angers University, and a Senior Researcher at the Institute for Theoretical and Experimental Physics in Moscow.
"About this title" may belong to another edition of this title.
- PublisherCambridge University Press
- Publication date2007
- ISBN 10 0521824761
- ISBN 13 9780521824767
- BindingHardcover
- LanguageEnglish
- Edition number1
- Number of pages518
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Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications)
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Cambridge University Press, 2007
ISBN 10: 0521824761
ISBN 13: 9780521824767
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Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications, Series Number 101)
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Cambridge University Press, 2007
ISBN 10: 0521824761
ISBN 13: 9780521824767
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Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications, Series Number 101)
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Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications, Series Number 101)
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Contact Geometry and Nonlinear Differential Equations
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Contact Geometry and Non-Linear Differential Equations
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Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications, Series Number 101)
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ISBN 13: 9780521824767
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Contact Geometry and Non-linear Differential Equations
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Contact Geometry and Non-Linear Differential Equations (Hardcover)
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ISBN 13: 9780521824767
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Hardcover. Condition: new. Hardcover. With the growing interest in the use of symmetry methods in applied mathematics, this book presents a comprehensive overview of the differential geometric view of the subject. The authors begin with a background chapter on calculus on manifolds, and then proceed to more advanced topics and applications, especially concerning singularities of the Monge-Ampere equations that describe many phenomena in geophysical fluid dynamics, for example. The authors describe many application areas and include computer code for implementing some of the techniques they describe. The book is richly illustrated. Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology). Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780521824767
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Contact Geometry and Non-Linear Differential Equations
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ISBN 10: 0521824761
ISBN 13: 9780521824767
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