Solitons Instantons and Twistors (Oxford Graduate Texts in Mathematics)  at Meripustak

Solitons Instantons and Twistors (Oxford Graduate Texts in Mathematics)

Books from same Author: Maciej Dunajski

Books from same Publisher: Oxford University Press

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  • General Information  
    Author(s) Maciej Dunajski
    PublisherOxford University Press
    Edition2nd Edition
    ISBN9780198872542
    Pages416
    BindingSoftcover
    Publish YearAugust 2024

    Description

    Oxford University Press Solitons Instantons and Twistors (Oxford Graduate Texts in Mathematics) by Maciej Dunajski

    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.