Zobrazeno 1 - 10
of 313
pro vyhledávání: '"Popovych, Roman"'
Nonlocal Hamiltonian operators of Ferapontov type are well-known objects that naturally arise local from Hamiltonian operators of Dubrovin-Novikov type with the help of three constructions, Dirac reduction, recursion scheme and reciprocal transformat
Externí odkaz:
http://arxiv.org/abs/2410.09669
Using an original method, we find the algebra of generalized symmetries of a remarkable (1+2)-dimensional ultraparabolic Fokker-Planck equation, which is also called the Kolmogorov equation and is singled out within the entire class of ultraparabolic
Externí odkaz:
http://arxiv.org/abs/2409.10348
We generalize the notion of semi-normalized classes of systems of differential equations, study properties of such classes and extend the algebraic method of group classification to them. In particular, we prove the important theorems on factoring ou
Externí odkaz:
http://arxiv.org/abs/2408.16897
Using the original advanced version of the direct method, we efficiently compute the equivalence groupoids and equivalence groups of two peculiar classes of Kolmogorov backward equations with power diffusivity and solve the problems of their complete
Externí odkaz:
http://arxiv.org/abs/2407.10356
Despite the number of relevant considerations in the literature, the algebra of generalized symmetries of the Burgers equation has not been exhaustively described. We fill this gap, presenting a basis of this algebra in an explicit form and proving t
Externí odkaz:
http://arxiv.org/abs/2406.02809
Autor:
Koval, Serhii D., Popovych, Roman O.
Publikováno v:
Stud. Appl. Math. 153 (2024), e12695
Within the class of (1+2)-dimensional ultraparabolic linear equations, we distinguish a fine Kolmogorov backward equation with a quadratic diffusivity. Modulo the point equivalence, it is a unique equation within the class whose essential Lie invaria
Externí odkaz:
http://arxiv.org/abs/2402.08822
Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods involve su
Externí odkaz:
http://arxiv.org/abs/2309.07899
Publikováno v:
Anal. Math. Phys. 14 (2024), 82
We exhaustively classify the Lie reductions of the real dispersionless Nizhnik equation to partial differential equations in two independent variables and to ordinary differential equations. Lie and point symmetries of reduced equations are comprehen
Externí odkaz:
http://arxiv.org/abs/2308.03744
Publikováno v:
Commun. Nonlinear Sci. Numer. Simul. 132 (2024), 107915
Applying an original megaideal-based version of the algebraic method, we compute the point-symmetry pseudogroup of the dispersionless (potential symmetric) Nizhnik equation. This is the first example of this kind in the literature, where there is no
Externí odkaz:
http://arxiv.org/abs/2211.09759
Autor:
Koval, Serhii D., Popovych, Roman O.
Publikováno v:
J. Math. Anal. Appl. 527 (2023), 127430
We derive a nice representation for point symmetry transformations of the (1+1)-dimensional linear heat equation and properly interpret them. This allows us to prove that the pseudogroup of these transformations has exactly two connected components.
Externí odkaz:
http://arxiv.org/abs/2208.11073