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The Resource Solitons, instantons, and twistors, Maciej Dunajski

Solitons, instantons, and twistors, Maciej Dunajski

Creator
Summary
"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, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basic differential geometry, complex manifold theory, and the exterior differential system."--BOOK JACKET
Language
eng
Work
Publication
Extent
xi, 359 pages
Contents
  • 5.
  • Lagrangian formalism and field theory
  • 6.
  • Gauge field theory
  • 7.
  • Integrability of ASDYM and twistor theory
  • 8.
  • Symmetry reductions and the integrable chiral model
  • 9.
  • Gravitational instantons
  • 1.
  • 10.
  • Anti-self-dual conformal structures
  • Appendix A.
  • Manifolds and topology
  • Appendix B.
  • Complex analysis
  • Appendix C.
  • Overdetermined PDEs
  • Integrability in classical mechanics
  • 2.
  • Soliton equations and the inverse scattering transform
  • 3.
  • Hamiltonian formalism and zero-curvature representation
  • 4.
  • Lie symmetries and reductions
Isbn
9780198570622
Instance
Label
Solitons, instantons, and twistors
Title
Solitons, instantons, and twistors
Statement of responsibility
Maciej Dunajski
Creator
Subject
Language
eng
Summary
"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, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basic differential geometry, complex manifold theory, and the exterior differential system."--BOOK JACKET
Member of
Cataloging source
DLC
http://library.link/vocab/creatorName
Dunajski, Maciej
Dewey number
530.12/4
Illustrations
illustrations
Index
index present
LC call number
QC174.26.W28
LC item number
D86 2010
Literary form
non fiction
Nature of contents
bibliography
Series statement
  • Oxford mathematics
  • Oxford graduate texts in mathematics ; 19
http://library.link/vocab/subjectName
  • Solitons
  • Geometry, Differential
  • Wave-motion, Theory of
  • Twistor theory
Label
Solitons, instantons, and twistors, Maciej Dunajski
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 5.
  • Lagrangian formalism and field theory
  • 6.
  • Gauge field theory
  • 7.
  • Integrability of ASDYM and twistor theory
  • 8.
  • Symmetry reductions and the integrable chiral model
  • 9.
  • Gravitational instantons
  • 1.
  • 10.
  • Anti-self-dual conformal structures
  • Appendix A.
  • Manifolds and topology
  • Appendix B.
  • Complex analysis
  • Appendix C.
  • Overdetermined PDEs
  • Integrability in classical mechanics
  • 2.
  • Soliton equations and the inverse scattering transform
  • 3.
  • Hamiltonian formalism and zero-curvature representation
  • 4.
  • Lie symmetries and reductions
Control code
320199531
Dimensions
25 cm
Extent
xi, 359 pages
Isbn
9780198570622
Lccn
2009032333
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)320199531
Label
Solitons, instantons, and twistors, Maciej Dunajski
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 5.
  • Lagrangian formalism and field theory
  • 6.
  • Gauge field theory
  • 7.
  • Integrability of ASDYM and twistor theory
  • 8.
  • Symmetry reductions and the integrable chiral model
  • 9.
  • Gravitational instantons
  • 1.
  • 10.
  • Anti-self-dual conformal structures
  • Appendix A.
  • Manifolds and topology
  • Appendix B.
  • Complex analysis
  • Appendix C.
  • Overdetermined PDEs
  • Integrability in classical mechanics
  • 2.
  • Soliton equations and the inverse scattering transform
  • 3.
  • Hamiltonian formalism and zero-curvature representation
  • 4.
  • Lie symmetries and reductions
Control code
320199531
Dimensions
25 cm
Extent
xi, 359 pages
Isbn
9780198570622
Lccn
2009032333
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)320199531

Subject

Member of

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