31 citations · 107 across the 11 of their papers we have counts for
11 papers
On a class of 3D second-order integrable Lagrangians and their dispersive deformations
Lingling Xue, E. V. Ferapontov, M. V. Pavlov
We investigate integrability of Euler-Lagrange equations associated with 3D second-order Lagrangians of the form \begin{equation*} \int f(u_{xy},u_{xt},u_{yt})\ \text{d}x\text{d}y\…
Lagrangian formulation of the Darboux system
Lingling Xue, E. V. Ferapontov, M. V. Pavlov
The classical Darboux system governing rotation coefficients of three-dimensional metrics of diagonal curvature possesses an equivalent formulation as a sixth-order PDE for a scala…
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…
Integrable systems of the intermediate long wave type in 2+1 dimensions
B. Gormley, E. V. Ferapontov, V. S. Novikov +1
We classify 2+1 dimensional integrable systems with nonlocality of the intermediate long wave type. Links to the 2+1 dimensional waterbag system are established. Dimensional reduct…
Second-order integrable Lagrangians and WDVV equations
Evgeny V. Ferapontov, Maxim V. Pavlov, Lingling Xue
We investigate integrability of Euler-Lagrange equations associated with 2D second-order Lagrangians of the form \begin{equation*} \int f(u_{xx},u_{xy},u_{yy})\ dxdy. \end{equation…
Remarks on the Lagrangian representation of bi-Hamiltonian equations
M. V. Pavlov, R. F. Vitolo
The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian b…
Towards the classification of homogeneous third-order Hamiltonian operators
E. V. Ferapontov, M. V. Pavlov, R. F. Vitolo
Let be a vector space of dimension . We demonstrate that -component third-order Hamiltonian operators of differential-geometric type are parametrised by the algebraic v…
Linearly Degenerate Hamiltonian PDEs and a New Class of Solutions to the WDVV Associativity Equations
B. A. Dubrovin, M. V. Pavlov, S. A. Zykov
We define a new class of solutions to the WDVV associativity equations. This class is determined by the property that one of the commuting PDEs associated with such a WDVV solution…
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…
Integrable Systems and Metrics of Constant Curvature
Maxim V. Pavlov
In this article we present a Lagrangian representation for evolutionary systems with a Hamiltonian structure determined by a differential-geometric Poisson bracket of the first ord…
Multi-Lagrangians for Integrable Systems
Y. Nutku, M. V. Pavlov
We propose a general scheme to construct multiple Lagrangians for completely integrable non-linear evolution equations that admit multi- Hamiltonian structure. The recursion operat…