Classification of Nonlinear Second-Order Differential Equations Admitting Certain First Integrals

Student: Kozlova Elizaveta

Supervisor: Dmitry Sinelshchikov

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

Educational Programme: Applied Mathematics (Bachelor)

Year of Graduation: 2021

In this paper, a family of Lienard equations is considered. The form of the equations of this family is determined, in which the first integral that is quadratic function with respect to the first derivative. In an explicit form, necessary and sufficient conditions for the members of this family are found to admit these integrals. The conditions for the equations of the considered family are derived to have a Lax representation with an L matrix with zero trace, and their equivalence with the conditions for the existence of a quadratic first integral is shown.

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