Nikolay Krylov (physicist)

Nikolay Mitrofanovich Krylov (Николай Митрофанович Крылов) (29 November 1879 – 11 May 1955) was a Soviet and Ukrainian mathematician and physicist, known for his work in interpolation, approximate methods for solving differential equations, and nonlinear mechanics. He significantly contributed to the development of the Bogoliubov–Krylov method (also known as the averaging method) for analyzing nonlinear oscillatory systems, developed with Nikolay Bogoliubov.

Krylov graduated from the Saint Petersburg Mining Institute in 1903 and became a professor at the same institute in 1912. He later worked at the Ukrainian Academy of Sciences, where he founded and directed the Institute of Mathematical Physics in Kiev.

His research covered a wide range of topics, including:

• Interpolation theory: Krylov developed methods for interpolating functions, particularly using trigonometric polynomials.

• Approximate methods for solving differential equations: He devised numerical and analytical techniques for finding approximate solutions to differential equations, which were crucial in various engineering and physics applications.

• Nonlinear mechanics: His most significant contribution was in this field, particularly the Bogoliubov-Krylov method. This method provides a powerful tool for analyzing the behavior of nonlinear oscillating systems by averaging over the rapid oscillations and obtaining simplified equations for the slow evolution of the system's amplitude and phase. This method has found applications in numerous areas, including radio engineering, mechanics, and plasma physics.

Krylov's work laid the foundation for many subsequent developments in nonlinear mechanics and continues to be relevant in contemporary research. He received numerous awards and honors for his scientific contributions.