208 citations · 891 across the 46 of their papers we have counts for
46 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…
Involutive scroll structures on solutions of 4D dispersionless integrable hierarchies
Evgeny Ferapontov, Boris Kruglikov
A rational normal scroll structure on an -dimensional manifold is defined as a field of rational normal scrolls of degree in the projectivised cotangent bundle $\m…
Hamiltonian aspects of the kinetic equation for soliton gas
Pierandrea Vergallo, Evgeny V. Ferapontov
We investigate Hamiltonian aspects of the integro-differential kinetic equation for dense soliton gas which results as a thermodynamic limit of the Whitham equations. Under a delta…
Defining differential equations for modular forms and Jacobi forms
Stanislav Opanasenko, Evgeny Ferapontov
It is well known that every modular form~ on a discrete subgroup satisfies a third-order nonlinear ODE that expresses algebraic dependence…
Hamiltonian systems of Jordan block type: delta-functional reductions of the kinetic equation for soliton gas
Pierandrea Vergallo, Evgeny V. Ferapontov
We demonstrate that linear degeneracy is a necessary condition for quasilinear systems of Jordan block type to possess first-order Hamiltonian structures. Multi-Hamiltonian formula…