74 citations · 309 across the 33 of their papers we have counts for
33 papers
On variational bivectors
I. S. Krasil'shchik
We construct examples of variational bivectors that are not Poissonian.
Integrability structures of the -dimensional Euler equation
I. S. Krasil'shchik, O. I. Morozov
We construct local and nonlocal Hamiltonian structures and variational symplectic structures for the -dimensional Euler equation in the vorticity form and study the action o…
The Calogero--Bogoyavlenskii--Schiff breaking soliton equation: recursion operators and higher symmetries
I. S. Krasil'shchik, O. I. Morozov
We find two one-parametric families of recursion operators and use them to construct higher symmetries for the Calogero--Bogoyavlenskii--Schiff breaking soliton equation. Then we p…
Lagrangian extensions of multi-dimensional integrable equations. I. The five-dimensional Mart{\'ı}nez Alonso--Shabat equation
I. S. Krasil'shchik, O. I. Morozov
We study a Lagrangian extension of the 5d Martínez Alonso--Shabat equation \begin{equation*} u_{yz}=u_{tx}+u_y\,u_{xs}-u_x\,u_{ys} \end{equation*} that coincides with…
On recursion operators for symmetries of the Pavlov-Mikhalev equation
I. S. Krasil'shchik
In geometry of nonlinear partial differential equations, recursion operators that act on symmetries of an equation are understood as Bäcklund auto-transformations of…
Recursion operators in the cotangent covering of the rdDym equation
I. S. Krasil'shchik, A. M. Verbovetsky
We describe a general method of constructing nonlocal recursion operators for symmetries of PDEs. As an example, the cotangent equation to the 3D rdDym equation $u_{yt} = u_xu_{xy}…