18 citations · 63 across the 10 of their papers we have counts for
10 papers
Extended group analysis and conservation laws of a class of variable coefficient generalized Kawahara equations
Olena Vaneeva, Alexander Zhalij, Olena Magda +1
We review and extend the results on the group analysis of a class of generalized Kawahara equations with time-dependent coefficients. First, we provide an overview of the existing…
Equivalence groupoid and enhanced group classification of a class of generalized Kawahara equations
Olena Vaneeva, Olena Magda, Alexander Zhalij
Transformation properties of a class of generalized Kawahara equations with time-dependent coefficients are studied. We construct the equivalence groupoid of the class and prove th…
Classification of reduction operators and exact solutions of variable coefficient Newell-Whitehead-Segel equations
Olena Vaneeva, Vyacheslav Boyko, Alexander Zhalij +1
A class of the Newell-Whitehead-Segel equations (also known as generalized Fisher equations and Newell-Whitehead equations) is studied with Lie and "nonclassical" symmetry points o…
Group classification of variable coefficient quasilinear reaction-diffusion equations
Olena Vaneeva, Alexander Zhalij
The group classification of variable coefficient quasilinear reaction-diffusion equations is carried out exhaustively. This became possible due to usage of a…
Quantum integrable systems in three-dimensional magnetic fields: the Cartesian case
Alexander Zhalij
In this paper we construct integrable three-dimensional quantum-mechanical systems with magnetic fields, admitting pairs of commuting second-order integrals of motion. The case of…
Separable unsteady nonparallel flow stability problems
Georgy Burde, Alexander Zhalij
The so-called 'direct' approach to separation of variables in linear PDEs is applied to the hydrodynamic stability problem. Calculations are made for the complete linear stability…