69 citations · 148 across the 9 of their papers we have counts for
6 papers · 1 filter
Lie group analysis for multi-scale plasma dynamics
Vladimir F. Kovalev
An application of approximate transformation groups to study dynamics of a system with distinct time scales is discussed. The utilization of the Krylov-Bogoliubov-Mitropolsky metho…
Group Analysis of Nonlinear Internal Waves in Oceans. II: The symmetries and rotationally invariant solution
Nail H. Ibragimov, Ranis N. Ibragimov, Vladimir F. Kovalev
74J30The maximal group of Lie point symmetries of a system of nonlinear equations used in geophysical fluid dynamics is presented. The Lie algebra of this group is infinite-dimensi…
Renormalization-group symmetries for solutions of nonlinear boundary value problems
V. F. Kovalev, D. V. Shirkov
Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concept…
Renormgroup symmetry for solution functionals
D. V. Shirkov, V. F. Kovalev
The paper contains generalization of the renormgroup algorithm for boundary value problems of mathematical physics and related concept of the renormgroup symmetry, formulated earli…
Symmetries of Integro-Differential Equations: A Survey of Methods Illustrated by the Benney Equations
N. H. Ibragimov, V. F. Kovalev, V. V. Pustovalov
Classical Lie group theory provides a universal tool for calculating symmetry groups for systems of differential equations. However Lie's method is not as much effective in the cas…
Functional self-similarity and renormalization group symmetry in mathematical physics
Vladimir F. Kovalev, Dmitrij V. Shirkov
The result from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during…