vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2026-62-1-27-37vestifm-873Research ArticleМАТЕМАТИКАMATHEMATICSПреобразования эквивалентности семейств квазилинейных эллиптических уравнений второго порядка функции двух переменныхEquivalence transformations of families of quasi-linear elliptic equations of the second order of a function of two variableshttps://orcid.org/0000-0001-5021-550XЖалукевичД. С.ZhalukevichD. S.

Жалукевич Денис Станиславович – соискатель, отдел дифференциальных уравнений

ул. Сурганова, 11, 220072, Минск

Dzianis S. Zhalukevich – Applicant, Department of Differential Equations

11, Surganov Str., 220072, Minsk

den.zhal@yandex.byИнститут математики Национальной академии наук БеларусиБеларусьInstitute of Mathematics of the National Academy of Sciences of BelarusBelarus2026310320266212737Copyright © Жалукевич Д.С., 20262026Жалукевич Д.С.Zhalukevich D.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/873

Исследованы инфинитезимальные преобразования эквивалентности 16 семейств квазилинейных эллиптических уравнений второго порядка функции двух переменных. Для семейств уравнений utt + uxx = f(t,x,u), utt + uxx = f(x,u) проведена симметрийная редукция.

In this work, we search for infinitesimal equivalence transformations of 16 families of quasi-linear elliptic equations of the second order in two variables. A symmetry reduction has been performed for the families of equations utt + uxx = f(t,x,u), utt + uxx = f(x,u).

эллиптическое уравнение Клейна – Гордонауравнение Братуквазилинейные уравненияпреобразования эквивалентностиредукция дифференциальных уравненийelliptic Klein – Gordon equationBratu equationquasi-linear equationsequivalence transformationsreduction of differential equationsReferencesZhalukevich, D. S. Equivalence transformations of families of second-order quasi-linear hyperbolic equations of two variables / D. S. Zhalukevich // Arxiv [Preprint] – 2025. – URL: https://www.researchgate.net/publication/398918025_Equivalence_transformations_of_families_of_second-order_quasi-linear_hyperbolic_equations_of_two_variables.Zhalukevich D. S. Equivalence transformations of families of second-order quasi-linear hyperbolic equations of two variables. Arxiv [Preprint], 2025. Available at: https://www.researchgate.net/publication/398918025_Equivalence_transformations_of_families_of_second-order_quasi-linear_hyperbolic_equations_of_two_variables.Zhalukevich, D. S. 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The authors declare that there are no conflicts of interest present.