46 citations · 306 across the 40 of their papers we have counts for
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A Lax representation, symmetries, and conservation laws for the three-dimensional Euler--Helmholtz equations
Oleg I. Morozov
We consider the three-dimensional Euler--Helmholtz equations for an inviscid incompressible fluid. Under the Poincar{é} lemma assumption, the incompressibility condition is resolve…
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…
Extensions of the symmetry algebra and Lax representations for the two-dimensional Euler equation
Oleg I. Morozov
We find the twisted extensions of the symmetry algebra of the 2D Euler equation in the vorticity form and use them to construct new Lax representation for this equation. Then we ge…
Lax representations for the magnetohydrodynamics equations
Oleg I. Morozov
We find two Lax representations for the reduced magnetohydrodynamics equations ({\sc rmhd}) and derive a B{ä}cklund transformation between the tangent and the cotangent coverings o…
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…
Integrable partial differential equations and Lie--Rinehart algebras
Oleg I. Morozov
We develop the method for constructing Lax representations of PDEs via the twisted extensions of their algebras of contact symmetries by generalizing the construction to the Lie--R…