Related papers: Dispersionless integrable systems and the Bogomoln…
For several classes of second order dispersionless PDEs, we show that the symbols of their formal linearizations define conformal structures which must be Einstein-Weyl in 3D (or self-dual in 4D) if and only if the PDE is integrable by the…
Using diffeomorphism group vector fields on $\mathbb{C}$-multiplied tori and the related Lie-algebraic structures, we study multi-dimensional dispersionless integrable systems that describe conformal structure generating equations of…
We investigate dispersionless integrable systems in 3D associated with fourfolds in the Grassmannian Gr(3,5). Such systems appear in numerous applications in continuum mechanics, general relativity and differential geometry, and include…
A dispersionless integrable system underlying 2+1-dimensional hyperCR Einstein--Weyl structures is obtained as a symmetry reduction of the anti--self--dual Yang--Mills equations with the gauge group Diff$(S^1)$. Two special classes of…
Einstein-Weyl geometry is a triple (D,g,w), where D is a symmetric connection, [g] is a conformal structure and w is a covector such that: (i) connection D preserves the conformal class [g], that is, Dg=wg; (ii) trace-free part of the…
We consistently develop a recently proposed scheme of matrix extension of dispersionless integrable systems for the general case of multidimensional hierarchies, concentrating on the case of dimension $d\geqslant 4$. We present extended Lax…
We introduce a dispersionless integrable system which interpolates between the dispersionless Kadomtsev-Petviashvili equation and the hyper-CR equation. The interpolating system arises as a symmetry reduction of the anti--self--dual…
Interpretation of dispersionless integrable hierarchies as equations of coisotropic deformations for certain algebras and other algebraic structures like Jordan triple systInterpretation of dispersionless integrable hierarchies as equations…
We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS$_{3}$ algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions. The analysis…
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 twistor methods has been established by…
We use a recently proposed scheme of matrix extension of dispersionless integrable systems for the Abelian case, in which it leads to linear equations, connected with the initial dispersionless system. In the examples considered, these…
Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian…
We present a method of constructing discrete integrable systems with crystallographic reflection group (Weyl) symmetries, thus clarifying the relationship between different discrete integrable systems in terms of their symmetry groups.…
From a specific series of exchange conditions for a one-parameter Hamiltonian vector field, we establish an integrable hierarchy using Lax pairs derived from the dispersionless partial differential equation. An exterior differential form of…
We present two constructions of new solutions to the dispersionless KP (dKP) equation arising from the first two Painlev\'e transcendents. The first construction is a hodograph transformation based on Einstein--Weyl geometry, the…
We construct a map of solutions of the dispersionless BKP (dBKP) equation to solutions of the Manakov-Santini (MS) system. This map defines an Einstein-Weyl structure corresponding to the dBKP equation through the general Lorentzian…
It was demonstrated recently [Dunajski, Ferapontov and Kruglikov (2014)] that the Manakov-Santini system describes a local form of general Lorentzian Einstein-Weyl geometry. We introduce integrable matrix extension of the Manakov-Santini…
Weyl derivatives, Weyl-Lie derivatives and conformal submersions are defined, then used to generalize the Jones-Tod correspondence between selfdual 4-manifolds with symmetry and Einstein-Weyl 3-manifolds with an abelian monopole. In this…
We present four examples of integrable partial differential equations (PDEs) of mathematical physics that---when linearized around a stationary soliton---exhibit scattering without reflection at {\it all} energies. Starting from the most…
Einstein-Weyl structures on a three-dimensional manifold $M$ is given by a system $E$ of PDEs on sections of a bundle over $M$. This system is invariant under the Lie pseudogroup $G$ of local diffeomorphisms on $M$. Two Einstein-Weyl…