Аннотация:A Study of a Mathematical Model with a Movable Singular Point in a Fourth-Order Nonlinear Differential EquationReceived 16 June 2023; accepted 29 August 2023; published 22 September 2023Author(s): Gasanov M., Gulkanov A.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 existence, necessary and sufficient conditions, Cauchy problemCitation: Gasanov M., Gulkanov A., A Study of a Mathematical Model with a Movable Singular Point in a Fourth-Order Nonlinear Differential Equation, Rus. J. Nonlin. Dyn., 2023 https://doi.org/10.20537/nd230904