Magomedyusuf Gasanov

    Yaroslavskoe shosse 26, Moscow city, Russia
    National Research Moscow State University of Civil


    Gasanov M. V., Gulkanov A. G., Modestov K. A.
    In this paper, we consider a mathematical model of the dynamics of the behavior of a spherically symmetric Rayleigh – Plesset bubble in the van der Waals gas model. The analysis of the model takes into account various isoprocesses without the presence of condensation and a model that takes into account condensation in an isothermal process. In each case, various characteristics are searched for, such as oscillation frequency (linear/small oscillations), damping factor, relaxation time, decrement, and logarithmic decrement. Solutions are found in quadratures for various parameters of the equation. The theoretical results obtained are compared with the results of the numerical solution of the Cauchy problem for various isoprocesses.
    Keywords: nonlinear differential equations, exact solution, small fluctuations, van der Waals equation, Rayleigh – Plesset equation
    Citation: Gasanov M. V., Gulkanov A. G., Modestov K. A.,  Analytical Solution of the Rayleigh – Plesset Equation Filled with Van Der Waals Gas for Various Isoprocesses, Rus. J. Nonlin. Dyn., 2024, Vol. 20, no. 1, pp.  3-13
    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.
    Keywords: nonlinear differential equations, movable singular point, exact criteria of existence, necessary and sufficient conditions, Cauchy problem
    Citation: Gasanov M. V., Gulkanov A. G.,  A Study of a Mathematical Model with a Movable Singular Point in a Fourth-Order Nonlinear Differential Equation, Rus. J. Nonlin. Dyn., 2023, Vol. 19, no. 4, pp.  575-584

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