Solitons, Instantons, and Twistors (Oxford Graduate Texts in Mathematics Book 19) by Maciej Dunajski (PDF)

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 lowerspace-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 overdeterminedsystems 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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a well written book that goes over a large range of material, including integrable systems, ASDYM equations, twistor theory, and applications to gravity. It is clearly written, and is a good advanced text on this material.

⭐This lecture series enabled me to understand the mathematics underlying these areas. Very interesting book and well worth the price

⭐

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