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Lectures of leading scientists at the Ural Mathematical Center (N.A. Kudryashov)

An online lecture entitled "Painlevé Test and Analytical Solutions of the Korteweg–de Vries–Burgers Equation with a Nonlinear Source" was held on July 22. The lecture was delivered by Nikolai Alekseevich Kudryashov, Professor at the National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) and Doctor of Physical and Mathematical Sciences.

In his talk, Nikolai Alekseevich presented methods for finding analytical solutions to nonlinear differential equations that can be systematized within a unified framework. Historically, this approach traces its origins to the work of Sofia Kovalevskaya, who studied the motion of a rigid body in a gravitational field. It was at that time that the Painlevé property — the absence of movable critical singular points in the general solution of an ordinary differential equation (ODE) — was first utilized.

Special attention was given to the application of the Painlevé test for analyzing the Korteweg–de Vries–Burgers equation with a nonlinear source. Professor Kudryashov examined the key aspects of the method in detail and demonstrated its effectiveness in the study of such equations.