22 citations · 34 across the 8 of their papers we have counts for
6 papers · 1 filter
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…
Towards classification of quasi-local symmetries of evolution equations
Renat Zhdanov
We develop efficient group-theoretical approach to the problem of classification of evolution equations that admit non-local transformation groups (quasi-local symmetries), i.e., g…
Group classification of the general evolution equation: local and quasi-local symmetries
Renat Zhdanov, Victor Lahno
We expand our group classification of quasilinear evolution equations (Acta Appl.Math., v.69, 2001) to the case of general evolution equation in one spatial variable. This enables…
Group classification of nonlinear wave equations
V. I. Lagno, R. Z. Zhdanov, O. Magda
We perform complete group classification of the general class of quasi linear wave equations in two variables. This class may be seen as a broad generalization of the nonlinear d'A…