Solitons, Instantons, and Twistors by Dunajski, Maciej
Solitons, Instantons, and Twistors by Dunajski, Maciej

Solitons, Instantons, and Twistors

Most nonlinear differential equations arising in natural sciences admit chaotic behaviour and cannot be solved analytically. Integrable...
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SKU: 9780198872535
Product Type: Books
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Author: Maciej Dunajski
Format: Hardcover
Language: English
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Solitons, Instantons, and Twistors by Dunajski, Maciej

Solitons, Instantons, and Twistors

$464.43
Solitons, Instantons, and Twistors by Dunajski, Maciej

Solitons, Instantons, and Twistors

$464.43
Author: Maciej Dunajski
Format: Hardcover
Language: English
Description
Most nonlinear differential equations arising in natural sciences admit chaotic behaviour 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, vortices, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basic differential geometry, complex manifold theory, and the exterior differential system.

Author: Maciej Dunajski
Publisher: Oxford University Press
Published: 09/24/2024
Pages: 416
Binding Type: Hardcover
Weight: 1.80lbs
Size: 8.90h x 6.50w x 1.70d
ISBN: 9780198872535

About the Author
Maciej Dunajski, Professor of Mathematical Physics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge

Maciej Dunajski is a Fellow of Clare College, and a Professor of Mathematical Physics at the Department of Applied Mathematics and Theoretical Physics, at the University of Cambridge. His research interests are in differential and projective Geometry, Solitons, and General Theory of Relativity. In 2021 he was awarded the Atiyah Fellowship by the London Mathematical Society. Dunajski is the winner of the 2023 Gravity Research Foundation Award, and the author of Geometry: A Very Short Introduction (OUP 2022).

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