39 citations · 308 across the 22 of their papers we have counts for
14 papers · 1 filter
Kinetic equation for soliton gas: integrable reductions
E. V. Ferapontov, M. V. Pavlov
Macroscopic dynamics of soliton gases can be analytically described by the thermodynamic limit of the Whitham equations, yielding an integro-differential kinetic equation for the d…
Second-order PDEs in 3D with Einstein-Weyl conformal structure
Sobhi Berjawi, Eugene Ferapontov, Boris Kruglikov +1
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…
Integrable systems in 4D associated with sixfolds in Gr(4,6)
Boris Doubrov, Eugene Ferapontov, Boris Kruglikov +1
Let be the Grassmannian of -dimensional linear subspaces of an -dimensional vector space . A submanifold gives rise to a differential system…
On a class of integrable systems of Monge-Ampère type
Boris Doubrov, Eugene Ferapontov, Boris Kruglikov +1
We investigate a class of multi-dimensional two-component systems of Monge-Ampère type that can be viewed as generalisations of heavenly-type equations appearing in self-dual Ricci…
Projective-geometric aspects of homogeneous third-order Hamiltonian operators
Eugene V. Ferapontov, Maxim V. Pavlov, Raffaele F. Vitolo
We investigate homogeneous third-order Hamiltonian operators of differential-geometric type. Based on the correspondence with quadratic line complexes, a complete list of such oper…
On the central quadric ansatz: integrable models and Painleve reductions
E. V. Ferapontov, B. Huard, A. Zhang
It was observed by Tod and later by Dunajski and Tod that the Boyer-Finley (BF) and the dispersionless Kadomtsev-Petviashvili (dKP) equations possess solutions whose level surfaces…
Integrable equations in 2+1-dimensions: deformations of dispersionless limits
E. V. Ferapontov, A. Moro, V. S. Novikov
We classify integrable third order equations in 2+1 dimensions which generalize the examples of Kadomtsev-Petviashvili, Veselov-Novikov and Harry Dym equations. Our approach is bas…
Dispersive deformations of hydrodynamic reductions of 2D dispersionless integrable systems
E. V. Ferapontov, A. Moro
We demonstrate that hydrodynamic reductions of dispersionless integrable systems in 2+1 dimensions, such as the dispersionless Kadomtsev-Petviashvili (dKP) and dispersionless Toda…
Classification of integrable Hamiltonian hydrodynamic chains associated with Kupershmidt's brackets
E. V. Ferapontov, K. R. Khusnutdinova, D. G. Marshall +1
We characterize a class of integrable Hamiltonian hydrodynamic chains, based on the necessary condition for the integrability provided by the vanishing of the Haantjes tensor. We p…
Double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability
E. V. Ferapontov, K. R. Khusnutdinova
An invariant differential-geometric approach to the integrability of (2+1)-dimensional systems of hydrodynamic type u_t+A(u)u_x+B(u)u_y=0 is developed. It is proved that the existe…
Hydrodynamic reductions of the heavenly equation
E. V. Ferapontov, M. V. Pavlov
We demonstrate that Plebański's first heavenly equation decouples in infinitely many ways into a triple of commuting (1+1)-dimensional systems of hydrodynamic type which satisfy th…
Reciprocal transformations of Hamiltonian operators of hydrodynamic type: nonlocal Hamiltonian formalism for linearly degenerate systems
E. V. Ferapontov, M. V. Pavlov
Reciprocal transformations of Hamiltonian operators of hydrodynamic type are investigated. The transformed operators are generally nonlocal, possessing a number of remarkable algeb…
Projective differential geometry of higher reductions of the two-dimensional Dirac equation
L. V. Bogdanov, E. V. Ferapontov
We investigate reductions of the two-dimensional Dirac equation imposed by the requirement of the existence of a differential operator of order mapping its eigenfunctions…
Decomposition of higher order equations of Monge-Ampere type
E. V. Ferapontov
Given a function f(x, t), its fourth (symmetric) differential is a quartic form in dx, dt. It is well-known that any quartic form in two variables can be represented as a sum of th…