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Review of exact solutions and reductions of Monge-Ampere type equationsстатья
Информация о цитировании статьи получена из
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 8 октября 2025 г.
- Авторы: Aksenov A.V., Polyanin A.D.
- Журнал: Theoretical and Mathematical Physics
- Том: 224
- Номер: 3
- Год издания: 2025
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 1527
- Последняя страница: 1566
- Оригинальные версии: Обзор по точным решениям и редукциям уравнений типа Монжа–Ампера
- DOI: 10.1134/S0040577925090028
- Аннотация: We present a review of publications devoted to exact solutions, transformations, symmetries, reductions,and applications of strongly nonlinear stationary and nonstationary (parabolic) equations of the Monge–Amp`ere type. We study the strongly nonlinear nonstationary mathematical physics equations with three independent variables that contain a quadratic combination of second spatial derivatives of the Monge–Amp`ere type and an arbitrary degree of the first temporal derivative or an arbitrary function depending on this derivative. We study the symmetries of these equations using group analysis methods. We derive formulas that enable the construction of multiparameter families of solutions, based on simpler solutions. We consider two-dimensional and one-dimensional symmetry and nonsymmetry reductions, which transform the original equations into simpler partial differential equations with two independent variables, or toordinary differential equations and systems of such equations. Self-similar and other invariant solutions are described. Using generalized and functional separation of variables methods, we constructed several new exact solutions, many of which are expressed in elementary functions or in quadratures. Some solutions are obtained using auxiliary intermediate-point or contact transformations. These exact solutions can beused as test problems to verify the adequacy of and evaluate the accuracy of numerical and approximateanalytical methods for solving problems described by strongly nonlinear mathematical physics equations.
- Добавил в систему: Аксенов Александр Васильевич