13 citations · 15 across the 4 of their papers we have counts for
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Integrability and solvability of polynomial Liénard differential systems
Maria V. Demina
We provide the necessary and sufficient conditions of Liouvillian integrability for Liénard differential systems describing nonlinear oscillators with a polynomial damping and a po…
Invariant algebraic curves for Liénard dynamical systems revisited
Maria Demina
A novel algebraic method for finding invariant algebraic curves for a polynomial vector field in is introduced. The structure of irreducible invariant algebraic curv…
From Puiseux series to invariant algebraic curves: the FitzHugh-Nagumo model
Maria V. Demina
A relationship between Puiseux series satisfying an ordinary differential equation corresponding to a polynomial dynamical system and degrees of irreducible invariant algebraic cur…
Elliptic solutions in the Hénon - Heiles model
Maria V. Demina, Nikolai A. Kudryashov
Equations of motion corresponding to the Hénon - Heiles system are considered. A method enabling one to find all elliptic solutions of an autonomous ordinary differential equation…
Relations for zeros of special polynomials associated to the Painleve equations
Nikolai A. Kudryashov, Maria V. Demina
A method for finding relations for the roots of polynomials is presented. Our approach allows us to get a number of relations for the zeros of the classical polynomials and for the…
Newton polygons for finding exact solutions
Nikolai A. Kudryashov, Maria V. Demina
A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of the Newton polygons corresponding to nonlinear diff…