Geodesic
A Study of a Mathematical Model with a Movable Singular Point in a Fourth-Order Nonlinear Differential Equation
Russian journal of nonlinear dynamics, Tome 19 (2023) no. 4, pp. 575-584

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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.
Keywords: nonlinear differential equations, movable singular point, exact criteria of exis- tence, necessary and sufficient conditions, Cauchy problem 
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M. V. Gasanov; A. G. Gulkanov. A Study of a Mathematical Model with a Movable Singular Point in a Fourth-Order Nonlinear Differential Equation. Russian journal of nonlinear dynamics, Tome 19 (2023) no. 4, pp. 575-584. http://geodesic.mathdoc.fr/item/ND_2023_19_4_a7/