688 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Bogolyubov Institute for Theoretical PhysicsUA16 papers
- National Academy of Sciences of UkraineUA14 papers
- Taras Shevchenko National University of KyivUA11 papers
- Institute of MathematicsPL7 papers
- University of NottinghamGB4 papers
- F.D. Ovcharenko Institute of Biocolloidal ChemistryUA3 papers
- Institute for Nuclear ResearchRU3 papers
- Leibniz Institute for Solid State and Materials ResearchDE3 papers
- Leiden UniversityNL3 papers
- University of ConnecticutUS3 papers
- AGH University of KrakowPL2 papers
- Bielefeld UniversityDE2 papers
9 papers · 1 filter
Nonlinear systems of PDEs admitting infinite-dimensional Lie algebras and their connection with Ricci flows. II: The two-dimensional space case
Roman Cherniha, John R. King
The work is a natural continuation of that published in Stud Appl Math. 2024; 153:e12737. All possible two-components evolutions systems of (1+2)-dimensional second-order PDEs admi…
Analysis of a Mathematical Model for Fluid Transport in Poroelastic Materials in 2D Space
Roman Cherniha, Vasyl' Davydovych, Joanna Stachowska-Pietka +1
A mathematical model for the poroelastic materials (PEM) with the variable volume is developed in multidimensional case. Governing equations of the model are constructed using the…
On degenerate sigma-functions of genus two
Julia Bernatska, Dmitry Leykin
We obtain explicit expressions for genus 2 degenerate sigma-function in terms of genus sigma-function and elementary functions as solutions of a system of linear PDEs satisfied…
Harmonic analysis on Lagrangian manifolds of integrable Hamiltonian systems
Julia Bernatska, Petro Holod
For an integrable Hamiltonian system we construct a representation of the phase space symmetry algebra over the space of functions on a Lagrangian manifold. The representation is a…
Lie symmetries and reductions of multi-dimensional boundary value problems of the Stefan type
Roman Cherniha, Sergii Kovalenko
A new definition of Lie invariance for nonlinear multi-dimensional boundary value problems (BVPs) is proposed by the generalization of known definitions to much wider classes of BV…
Resonance in a driven two-level system: analytical results without the rotating wave approximation
Yu. V. Bezvershenko, P. I. Holod
We consider the problem of two-level system dynamics induced by the time-dependent field B={a(t)cosωt,a(t)sinωt,ω_0}, with a(t) \sim cn(νt,k). The problem is exactly analytically s…
Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system
Roman Cherniha, Vasyl' Davydovych
Q-conditional symmetries of the classical Lotka-Volterra system in the case of one space variable are completely described and a set of such symmetries in explicit form is construc…
Lie symmetries of nonlinear boundary value problems
Roman Cherniha, Sergii Kovalenko
Nonlinear boundary value problems (BVPs) by means of the classical Lie symmetry method are studied. A new definition of Lie invariance for BVPs is proposed by the generalization of…
Non-equilibrium stochastic dynamics of continuous systems and Bogoliubov generating functionals
Yuri G. Kondratiev, Tobias Kuna, Maria Joao Oliveira
Combinatorial harmonic analysis techniques are used to develop new functional analysis methods based on Bogoliubov functionals. Concrete applications of the methods are presented,…