191 citations · 597 across the 29 of their papers we have counts for
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Stationary mKdV hierarchy and integrability of the Dirac equations by quadratures
Renat Zhdanov, Ihor Revenko, Wilhelm Fushchych
Using the Lie's infinitesimal method we establish that the Dirac equation in one variable is integrable by quadratures if the potential V(x) is a solution of one of the equations o…
Integrability of Riccati equations and the stationary KdV equations
Renat Zhdanov
Using the S.Lie's infinitesimal approach we establish the connection between integrability of a one-parameter family of the Riccati equations and the stationary KdV hierarchy.
On Integrable Doebner-Goldin Equations
P. Nattermann, R. Zhdanov
We suggest a method for integrating sub-families of a family of nonlinear {\sc Schrödinger} equations proposed by {\sc H.-D.~Doebner} and {\sc G.A.~Goldin} in the 1+1 dimensional c…
On the new approach to variable separation in the time-dependent Schrödinger equation with two space dimensions
Renat Z. Zhdanov, Ihor V. Revenko, Wilhelm I. Fushchych
We suggest an effective approach to separation of variables in the Schrödinger equation with two space variables. Using it we classify inequivalent potentials such tha…
Conditional Lie-Bäcklund symmetry and reduction of evolution equations.
R. Z. Zhdanov
We suggest a generalization of the notion of invariance of a given partial differential equation with respect to Lie-Bäcklund vector field. Such generalization proves to be effecti…