Galoisian and qualitative approaches to linear Polyanin-Zaitsev vector fields

Galoisian and qualitative approaches to linear Polyanin-Zaitsev vector fields

In this paper we study a particular parametric family of differential equations, the so-called Linear Polyanin-Zaitsev Vector Field, which has been introduced in a general case in [1] as a correction of a family presented in [2]. Linear Polyanin-Zaitsev Vector Field is transformed into a Liénard equ...

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Bibliographic Details
Main Authors: Acosta-Humánez Primitivo B., Reyes-Linero Alberto, Rodriguez-Contreras Jorge
Format: Article
Language:English
Published: De Gruyter 2018-10-01
Series:Open Mathematics
Subjects:
integrability
qualitative
stability
critical point
polynomial
polyanin-zaitsev vector field
12h05
34c99
Online Access:https://doi.org/10.1515/math-2018-0102
Description
Summary:In this paper we study a particular parametric family of differential equations, the so-called Linear Polyanin-Zaitsev Vector Field, which has been introduced in a general case in [1] as a correction of a family presented in [2]. Linear Polyanin-Zaitsev Vector Field is transformed into a Liénard equation and, in particular, we obtain the Van Der Pol equation. We present some algebraic and qualitative results to illustrate some interactions between algebra and the qualitative theory of differential equations in this parametric family.
ISSN:2391-5455

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