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Oxford Graduate Texts in Mathematics #19: Solitons, Instantons, and Twistors. by Maciej Dunajski

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Oxford Graduate Texts in Mathematics #19: Solitons, Instantons, and Twistors. by Maciej Dunajski Cover

 

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Publisher Comments:

Most nonlinear differential equations arising in natural sciences admit chaotic behavior and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well behaved solutions known as solitons and instantons. These solutions play important roles in pure and applied mathematics as well as in theoretical physics where they describe configurations topologically different from vacuum. While integrable equations in lower space-time dimensions can be solved using the inverse scattering transform, the higher-dimensional examples of anti-self-dual Yang-Mills and Einstein equations require twistor theory. Both techniques rely on an ability to represent nonlinear equations as compatibility conditions for overdetermined systems of linear differential equations.

The book provides a self-contained and accessible introduction to the subject. It starts with an introduction to integrability of ordinary and partial differential equations. Subsequent chapters explore symmetry analysis, gauge theory, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basic differential geometry, complex manifold theory, and the exterior differential system.

About the Author

Maciej Dunajski read physics in Lodz, Poland and received a PhD in mathematics from Oxford University where he held a Senior Scholarship at Merton College. After spending four years as a lecturer in the Mathematical Institute in Oxford where he was a member of Roger Penrose's research group, he moved to Cambridge, where he holds a Fellowship and lectureship at Clare College and a Newton Trust Lectureship at the Department of Applied Mathematics and Theoretical Physics. Dunajski specialises in twistor theory and differential geometric approaches to integrability and solitons. He is married with two sons.

Table of Contents

Preface

1. Integrability in classical mechanics

2. Soliton equations and the Inverse Scattering Transform

3. The hamiltonian formalism and the zero-curvature representation

4. Lie symmetries and reductions

5. The Lagrangian formalism and field theory

6. Gauge field theory

7. Integrability of ASDYM and twistor theory

8. Symmetry reductions and the integrable chiral model

9. Gravitational instantons

10. Anti-self-dual conformal structures

Appendix A: Manifolds and Topology

Appendix B: Complex analysis

Appendix C: Overdetermined PDEs

Index

Product Details

ISBN:
9780198570639
Author:
Dunajski, Maciej
Publisher:
Oxford University Press, USA
Author:
null, Maciej
Subject:
Geometry - Differential
Subject:
Wave-motion, theory of
Subject:
Waves & Wave Mechanics
Subject:
Applied
Subject:
Mathematical Physics
Subject:
Mathematics | Pure Mathematics
Subject:
Physics-General
Series:
Oxford Graduate Texts in Mathematics
Series Volume:
19
Publication Date:
20100231
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
35 illus.
Pages:
368
Dimensions:
6.1 x 9.1 x 0.8 in 1.25 lb

Related Subjects


Science and Mathematics » Mathematics » Applied
Science and Mathematics » Physics » General
Science and Mathematics » Physics » Math

Oxford Graduate Texts in Mathematics #19: Solitons, Instantons, and Twistors. by Maciej Dunajski New Trade Paper
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