Solitons, Instantons, and Twistors

Maciej Dunajski read physics in Lodz, Poland and received a PhD in mathematics from Oxford University where he held a Senior Scholarship at Merton College. After spending four years as a lecturer in the Mathematical Institute in Oxford where he was a member of Roger Penrose's research group, he moved to Cambridge, where holds a Fellowship and lectureship at Clare College and a Newton Trust Lectureship at the Department of Applied Mathematics and Theoretical Physics. Dunajski specialises in twistor theory and differential geometric approaches to integrability and solitons. He is married with two sons.

• Preface ; 1. Integrability in classical mechanics ; 2. Soliton equations and the Inverse Scattering Transform ; 3. The hamiltonian formalism and the zero-curvature representation ; 4. Lie symmetries and reductions ; 5. The 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 ; 10. Anti-self-dual conformal structures ; Appendix A: Manifolds and Topology ; Appendix B: Complex analysis ; Appendix C: Overdetermined PDEs ; Index

My view is that the book is a success. I have no hesitation in recommending the book as a textbook/reference for advanced undergraduates (Mmath or other masters level), and for researchers as well. It is also very valuable as a crossover book: showing researchers in other disciplines how some of this new theory motivated by cosmology can be introduced into other areas such as fluid mechanics.