Exact solutions of a remarkable fin equation. - Roman O. Popovych; Christodoulos Sophocleous; Olena O. Vaneeva (Appl. Math. Lett., 2008)

Group analysis of nonlinear fin equations. - Olena O. Vaneeva; Andrew G. Johnpillai; Roman O. Popovych; Christodoulos Sophocleous (Appl. Math. Lett., 2008)

Invariant Discretization Schemes for the Shallow-Water Equations. - Alexander Bihlo; Roman O. Popovych (SIAM J. Sci. Comput., 2012)

Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping. - Oleksandr A. Pocheketa; Roman O. Popovych; Olena O. Vaneeva (Appl. Math. Comput., 2014)

Variational symmetries and conservation laws of the wave equation in one space dimension. - Roman O. Popovych; Alexei F. Cheviakov (Appl. Math. Lett., 2020)

Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations. - Olena O. Vaneeva; Alexander Bihlo; Roman O. Popovych (Commun. Nonlinear Sci. Numer. Simul., 2020)

Point and contact equivalence groupoids of two-dimensional quasilinear hyperbolic equations. - Roman O. Popovych (Appl. Math. Lett., 2021)

On the ineffectiveness of constant rotation in the primitive equations and their symmetry analysis. - Elsa Dos Santos Cardoso-Bihlo; Roman O. Popovych (Commun. Nonlinear Sci. Numer. Simul., 2021)

Physics-informed neural networks for the shallow-water equations on the sphere. - Alex Bihlo; Roman O. Popovych (J. Comput. Phys., 2022)

Improving physics-informed DeepONets with hard constraints. - Rüdiger Brecht; Dmytro R. Popovych; Alex Bihlo; Roman O. Popovych (CoRR, 2023)

Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation. - Vyacheslav M. Boyko; Roman O. Popovych; Oleksandra O. Vinnichenko (Commun. Nonlinear Sci. Numer. Simul., 2024)