Аннотация:
This article introduces a mathematical model that utilizes a nonlinear differential equation to
study a range of phenomena such as nonlinear wave processes, and beam deflections. Solving this
equation is challenging due to the presence of moving singular points. The article addresses two
main problems: first, it establishes the existence and uniqueness of the solution of the equation
and, second, it provides precise criteria for determining the existence of a moving singular point.
Additionally, the article presents estimates of the error in the analytical approximate solution
and validates the results through a numerical experiment.
Ключевые слова:
nonlinear differential equations, movable singular point, exact criteria of exis-
tence, necessary and sufficient conditions, Cauchy problem
Поступила в редакцию: 16.06.2023 Принята в печать: 29.08.2023
Образец цитирования:
M. V. Gasanov, A. G. Gulkanov, “A Study of a Mathematical Model with a Movable Singular Point in a Fourth-Order Nonlinear Differential Equation”, Rus. J. Nonlin. Dyn., 19:4 (2023), 575–584
\RBibitem{GasGul23}
\by M. V. Gasanov, A. G. Gulkanov
\paper A Study of a Mathematical Model with a Movable Singular Point in a Fourth-Order Nonlinear Differential Equation
\jour Rus. J. Nonlin. Dyn.
\yr 2023
\vol 19
\issue 4
\pages 575--584
\mathnet{http://mi.mathnet.ru/nd866}
\crossref{https://doi.org/10.20537/nd230904}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/nd866
https://www.mathnet.ru/rus/nd/v19/i4/p575
Эта публикация цитируется в следующих 1 статьяx:
Magomedyusuf Gasanov, Aleksandr Gulkanov, “INVESTIGATION OF A STRONGLY NONLINEAR OSCILLATOR WITH MOVABLE ALGEBRAIC SINGULARITIES”, J Math Sci, 2025