191 citations · 597 across the 29 of their papers we have counts for
29 papers
On realizations of the Witt algebra in
Renat Zhdanov, Qing Huang
We obtain exhaustive classification of inequivalent realizations of the Witt and Virasoro algebras by Lie vector fields of differential operators in the space . Using…
On realizations of the Virasoro algebra
Renat Zhdanov, Qing Huang
We obtain complete classification of in-equivalent realizations of the Virasoro algebra by Lie vector fields over the three-dimensional field of real numbers. As an application we…
On contact symmetries of evolution equations
Qing Huang, Renat Zhdanov, Changzheng Qu
In this paper, we develop an algebraic approach to classifying contact symmetries of the second-order nonlinear evolution equations. Up to contact isomorphisms, all inequivalent PD…
Nonlocal symmetries of evolution equations
Renat Zhdanov
We suggest the method for group classification of evolution equations admitting nonlocal symmetries which are associated with a given evolution equation possessing nontrivial Lie s…
Nonlocal symmetries of systems of evolution equations
Renat Zhdanov
We prove that any potential symmetry of a system of evolution equations reduces to a Lie symmetry through a nonlocal transformation of variables. Based on this fact is our method o…
On group classification of evolution equations admitting non-local symmetries
Renat Zhdanov
We prove that any evolution equation admitting a potential symmetry can always be reduced to another evolution equation such that the potential symmetry in question maps into the g…