Szczegóły publikacji
Opis bibliograficzny
Extended symmetry of the Witten-Dijkgraaf-Verlinde-Verlinde equation of Monge-Ampere type / Patryk SITKO, Ivan TSYFRA // Opuscula Mathematica ; ISSN 1232-9274. — Tytuł poprz.: Scientific Bulletins of Stanisław Staszic Academy of Mining and Metallurgy. Opuscula Mathematica. — 2025 — vol. 45 no. 2, s. 251–274. — Bibliogr. s. 272–274, Abstr. — Publikacja dostępna online od: 2025-03-10
Autorzy (2)
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 159823 |
|---|---|
| Data dodania do BaDAP | 2025-06-16 |
| Tekst źródłowy | URL |
| DOI | 10.7494/OpMath.2025.45.2.251 |
| Rok publikacji | 2025 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Opuscula Mathematica : rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica |
Abstract
We construct the Lie algebra of extended symmetry group for the Monge–Ampere type Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equation. This algebra includes novel generators that are unobtainable within the framework of the classical Lie approach and correspond to non-point group transformation of dependent and independent variables. The expansion of symmetry is achieved by introducing new variables through second-order derivatives of the dependent variable. By integrating the Lie equations, we derive transformations that enable the generation of new solutions to the Witten–Dijkgraaf–Verlinde–Verlinde equation from a known one. These transformations yield formulas for obtaining new solutions in implicit form and Bäcklund-type transformations for the nonlinear associativity equations. We also demonstrate that, in the case under study, introducing a substitution of variables via third-order derivatives, as previously used in the literature, does not yield generators of non-point transformations. Instead, this approach produces only the Lie groups of classical point transformations. Furthermore, we perform a group reduction of partial differential equations in two independent variables to a system of ordinary differential equations. This reduction leads to the explicit solution of the fully nonlinear differential equation. Notably, the symmetry group of non-point transformations expands significantly when this method is applied to the second-order differential equation, resulting in a corresponding infinite-dimensional Lie algebra. Finally, we show that auxiliary variables can be systematically derived within the framework of a generalized approach to symmetry reduction of differential equations.
