On Recursion Operators for Symmetries of the Pavlov–Mikhalev Equation

In geometry of nonlinear partial differential equations, recursion operators that act on symmetries an equation $$\mathcal{E}$$ are understood as Bäcklund auto-transformations the $$\mathcal{TE}$$ tangent to . We apply this approach a natural two-component extension 3D Pavlov–Mikhalev $$u_{yy}=u_{tx}+u_{y}u_{xx}-u_{x}u_{xy}.$$ describe Lie algebra for extension, construct two (one them was known earlier) and find their action. also establish hereditary property these well compatibility (in sense Frölicher–Nijenhuis bracket). twelve additional which degenerate in (we call queer) discuss properties. concluding part, geometrical background conservation laws multi-dimensional equations is exposed together with its relations coverings.