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The book provides a self-contained and accessible introduction to integrable systems. It starts with an introduction to integrability of ordinary and partial differential equations, and goes on to explore symmetry analysis, gauge theory, vortices, gravitational instantons, twistor transforms, and anti-self-duality equations.
List of contents
- 1: Integrability in classical mechanics
- 2: Soliton equations and the inverse scattering transform
- 3: Hamiltonian formalism and zero-curvature representation
- 4: Lie symmetries and reductions
- 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: Vortices
- 10: Gravitational instantons
- 11: Anti-self-dual conformal structures
About the author
Maciej Dunajski is a Fellow of Clare College, and a Professor of Mathematical Physics at the Department of Applied Mathematics and Theoretical Physics, at the University of Cambridge. His research interests are in differential and projective Geometry, Solitons, and General Theory of Relativity. In 2021 he was awarded the Atiyah Fellowship by the London Mathematical Society. Dunajski is the winner of the 2023 Gravity Research Foundation Award, and the author of
Geometry: A Very Short Introduction (OUP 2022).
Summary
The book provides a self-contained and accessible introduction to integrable systems. It starts with an introduction to integrability of ordinary and partial differential equations, and goes on to explore symmetry analysis, gauge theory, vortices, gravitational instantons, twistor transforms, and anti-self-duality equations.
Additional text
The great strength of this volume is how self-contained it is in its approach, one seldom needs to look elsewhere before delving headfirst into this volume. In my own work, this text is often my first go-to choice whenever I require reference.A particular strength of the text is its firm modern introduction to integrability, as well as its gentle and instructive introduction to gravitational instantons and twistor theory. This text is suitable for a graduate-level reader base whose education has at least included a first course in quantum field theory and general relativity.
