We review aspects of twistor theory, its aims and achievements spanning the last five
decades. In the twistor approach, space–time is secondary with events being derived …

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 …

A bstract The double copy relates scattering amplitudes and classical solutions in Yang-Mills
theory, gravity, and related field theories. Previous work has shown that this has an explicit …

It is shown that Einstein–Weyl (EW) equations in 2+ 1 dimensions contain the dispersionless
Kadomtsev–Petviashvili (dKP) equation as a special case: if an EW structure admits a …

HyperCR Einstein–Weyl equations in 2+ 1 dimensions reduce to a pair of quasi-linear PDEs
of hydrodynamic type. All solutions to this hydrodynamic system can in principle be …

For several classes of second-order dispersionless PDEs, we show that the symbols of their
formal linearizations define conformal structures that must be Einstein-Weyl in 3D (or self …

The equations governing anti-self-dual and Einstein-Weyl conformal geometries can be
regarded as “master dispersionless systems” in four and three dimensions, respectively …

We present a simple novel construction of recursion operators for integrable
multidimensional dispersionless systems that admit a Lax pair whose operators are linear in …

A twistor construction of the hierarchy associated with the hyper-Kähler equations on a
metric (the anti-self-dual Einstein vacuum equations, ASDVE, in four dimensions) is given …

We study integrable non-degenerate Monge–Ampère equations of Hirota type in 4D and
demonstrate that their symmetry algebras have a distinguished graded structure, uniquely …