Аннотация:
We discuss an algorithm for integrating systems of two second-order ordinary differential equations (ODE) with a small parameter that admit approximate Lie algebras with four essential generators. The algorithm is a modification of the method of consecutive order reduction and is based on using operators of invariant differentiation. A special attention is given to the peculiarities of its application in dependence of the structural properties of Lie algebras of approximate symmetries.
Ключевые слова:
system of two second-order ordinary differential equations with a small parameter, approximate Lie algebra of generators, operator of invariant differentiation, invariant representation, differential invariant, integration of equations.
Образец цитирования:
A. A. Gainetdinova, R. K. Gazizov, “Integration of systems of two second-order ordinary differential equations with a small parameter that admit four essential operators”, Сиб. электрон. матем. изв., 17 (2020), 604–614
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\by A.~A.~Gainetdinova, R.~K.~Gazizov
\paper Integration of systems of two second-order ordinary differential equations with a small parameter that admit four essential operators
\jour Сиб. электрон. матем. изв.
\yr 2020
\vol 17
\pages 604--614
\mathnet{http://mi.mathnet.ru/semr1234}
\crossref{https://doi.org/10.33048/semi.2020.17.039}
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https://www.mathnet.ru/rus/semr1234
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Эта публикация цитируется в следующих 2 статьяx:
阳 杨, “Existence and Uniqueness of Positive Solutions for a Class of Second-Order Nonlinear Differential Systems”, PM, 11:06 (2021), 1211
Jacob Manale, “On Solutions of the Nonlinear Heat Equation Using Modified Lie Symmetries and Differentiable Topological Manifolds”, WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS, 15 (2020), 132