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Integrable Systems
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
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
  • Mathematics
    Proceedings 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
On the Einstein-Weyl and conformal self-duality equations
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
Anti-self-dual Conformal Structures with Null Killing Vectors from Projective Structures
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
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
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