Solitons, instantons, and twistors / Maciej Dunajski.Material type: TextSeries: Oxford mathematics | Oxford graduate texts in mathematics ; 19.Publication details: Oxford ; New York : Oxford University Press, 2010. Description: 1 online resource (xi, 359 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9780191574108; 0191574104Subject(s): Solitons -- Mathematics | Instantons -- Mathematics | Wave-motion, Theory of | Geometry, Differential | Twistor theory | SCIENCE -- Waves & Wave Mechanics | Geometry, Differential | Solitons -- Mathematics | Twistor theory | Wave-motion, Theory ofGenre/Form: Electronic books. | Electronic books. Additional physical formats: Print version:: Solitons, instantons, and twistors.DDC classification: 530.12/4 LOC classification: QC174.26.W28 | D86 2010ebOnline resources: Click here to access online
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Includes bibliographical references and index.
Integrability in classical mathematics -- Soliton equations and the inverse scattering transform -- Hamiltonian formalism and zero-curvature representation -- Lie symmetries and reductions -- Lagrangian formalism and field theory -- Gauge field theory -- Integrability of ASDYM and twistor theory -- Symmetry reductions and the integrable chiral model -- Gravitational instantons -- Anti-self-dual conformal structures -- Appendix A: Manifolds and topology -- Appendix B: Complex analysis -- Appendix C: Overdetermined PDEs.
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-timedimensions can be solved using the inverse scattering transform, the higher-dimensional examples of anti-self-dual Yan.
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