A Study of a Mathematical Model with a Movable Singular Point in a Fourth-Order Nonlinear Differential Equation
Received 16 June 2023; accepted 29 August 2023; published 22 September 2023
2023, Vol. 19, no. 4, pp. 575-584
Author(s): Gasanov M. V., Gulkanov A. G.
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.
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