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Integrable Systems
- M. Dunajski
- Mathematics
- 2012
Many natural systems can be modelled by partial differential equations (PDEs), especially systems exhibiting wave-like phenomena. Such systems often have quantities that are conserved in time, common…
Solitons, Instantons, and Twistors
- M. Dunajski
- Mathematics
- 8 February 2010
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…
Anti-self-dual four–manifolds with a parallel real spinor
- M. Dunajski
- MathematicsProceedings of the Royal Society of London…
- 28 February 2001
Anti–self–dual metrics in the (++ ––) signature that admit a covariantly constant real spinor are studied. It is shown that finding such metrics reduces to solving a fourth–order integrable partial…
Einstein–Weyl geometry, the dKP equation and twistor theory
- M. Dunajski, L. Mason, P. Tod
- Mathematics
- 6 April 2000
On the Einstein-Weyl and conformal self-duality equations
- M. Dunajski, E. Ferapontov, B. Kruglikov
- Mathematics, Physics
- 30 May 2014
The equations governing anti-self-dual and Einstein-Weyl conformal geometries can be regarded as `master dispersionless systems' in four and three dimensions respectively. Their integrability by…
Einstein–Weyl structures from hyper–Kähler metrics with conformal Killing vectors
- M. Dunajski, P. Tod
- Mathematics, Physics
- 23 July 1999
A class of Einstein–Weyl spaces associated to an integrable system of hydrodynamic type
- M. Dunajski
- Mathematics, Physics
- 13 November 2003
Anti-self-dual Conformal Structures with Null Killing Vectors from Projective Structures
- M. Dunajski, Simon West
- Mathematics
- 17 January 2006
Using twistor methods, we explicitly construct all local forms of four–dimensional real analytic neutral signature anti–self–dual conformal structures (M, [g]) with a null conformal Killing vector.…
Cosmological Einstein-Maxwell instantons and euclidean supersymmetry: beyond self-duality
- M. Dunajski, J. Gutowski, W. Sabra, P. Tod
- Physics, Mathematics
- 6 December 2010
We construct new supersymmetric solutions to the Euclidean Einstein-Maxwell theory with a non-vanishing cosmological constant, and for which the Maxwell field strength is neither self-dual or…
Metrisability of three-dimensional projective structures
- R. Bryant, M. Dunajski, M. Eastwood
- Mathematics
- 1 January 2008
We carry out the programme of R. Liouville \cite{Liouville} to construct an explicit local obstruction to the existence of a Levi--Civita connection within a given projective structure $[\Gamma]$ on…
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