Zobrazeno 1 - 10
of 312
pro vyhledávání: '"Popovych, Roman"'
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.
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
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
We carry out the extended symmetry analysis of an ultraparabolic Fokker-Planck equation with three independent variables, which is also called the Kolmogorov equation and is singled out within the class of such Fokker-Planck equations by its remarkab
Externí odkaz:
http://arxiv.org/abs/2205.13526
Let $F_q$ be a field with $q$ elements, where $q$ is a power of a prime number $p\geq 5$. For any integer $m\geq 2$ and $a\in F_q^*$ such that the polynomial $x^m-a$ is irreducible in $F_q[x]$, we combine two different methods to construct explicitly
Externí odkaz:
http://arxiv.org/abs/2204.13882