The Darboux Theory of Integrability for a Nonlinear Oscillator with the Damping Linearly Depending on the Velocity

Student: Ischenko Anna

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Systems Analysis and Mathematical Technologies (Master)

Year of Graduation: 2024

In this work the Darboux theory of integrability is applied to study nonlinear cubic oscillators generalizing the Duffing —— Van der Pol oscillator. The classification of Darboux polynomials for the family of differential systems describing the oscillators under consideration is carried out. The necessary and sufficient conditions for the existence of Darboux first integrals and Darboux integrating factors in the non-degenerate case are obtained. Previously unknown integrable oscillators are found.

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