000			02098nam a22002657a 4500
005			20250707120125.0
008			250707b |||||||| |||| 00| 0 eng d
020			_a9780198872542
040			_aCSL _cCSL
041			_2eng _aeng
084			_aB85 R4 _qCSL
100			_aDunajski, Maciej _eauthor. _9815238
245			_aSolitons, Instantons, and Twistors
250			_a2nd ed.
260			_aOxford : _bOxford University Press, _c2024.
300			_axii, 393p. _b: ill. _c; 23 cm.
490			_aOxford Graduate Texts in Mathematics
500			_aIncludes appendix ,references and index.
520			_aMost 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.
650			_aSolitons. _9815239
650			_aIntegrable systems. _9815240
650			_aGauge fields theory. _9815241
650			_aTwistor theory. _9815242
942			_2CC _cTEXL _e2nd ed. _hB85 R4 _n0
999			_c1433457 _d1433457