We present a unified mathematical approach to the symbolic computation of integrability
structures of partial differential equations, like Hamiltonian operators, recursion operators for …

We present a new approach to construction of recursion operators for multidimensional
integrable systems which have a Lax-type representation in terms of a pair of commuting …

We present a review of differential-geometric and Lie-algebraic approaches to the
investigation of a broad class of nonlinear integrable differential systems of “heavenly” type …

We prove that integrability of a dispersionless Hirota-type equation implies the symplectic
Monge–Ampère property in any dimension. In 4D, this yields a complete classification of …

We discover two additional Lax pairs and three nonlocal recursion operators for symmetries
of the general heavenly equation introduced by Doubrov and Ferapontov. Converting the …

Abstract We consider (3+ 1)-dimensional second-order evolutionary PDEs where the
unknown u enters only in the form of the 2nd-order partial derivatives. For such equations …

We present first heavenly equation of Plebański in a two-component evolutionary form and
obtain Lagrangian and Hamiltonian representations of this system. We study all point …

In this work, we investigate a symmetry reduction of the recently discovered (3+ 1)-
dimensional equation of the Monge-Ampère type. This equation forms a bi-Hamiltonian …

Some new classes of exact solutions (so-called functionally invariant solutions) of the elliptic
and hyperbolic complex Monge–Ampère equations and of the second heavenly equation …

Using diffeomorphism group vector fields on $\mathbb {C} $-multiplied tori and the related
Lie-algebraic structures, we study multi-dimensional dispersionless integrable systems that …