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Volume 1, Issue 2
On the Integrability and Equivalence of the Abel Equation and Some Polynomial Equations

Yuexin Yan, Yingxin Pan, Feifei Lu & Zhengxin Zhou

DOI: 10.12150/jnma.2019.207

J. Nonl. Mod. Anal., 1 (2019), pp. 207-220.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, first of all we give the necessary and sufficient conditions of the center of a class of planar quintic differential systems by using reflecting function method, and provide a simple proof of this results. Secondly, We use the reflecting integral to research the equivalence of the Abel equation and some complicated equations and derive their center conditions and discuss their integrability.

  • Keywords

Center condition, integrability, reflecting integral, equivalence.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{JNMA-1-207, author = {Yan , YuexinPan , YingxinLu , Feifei and Zhou , Zhengxin}, title = {On the Integrability and Equivalence of the Abel Equation and Some Polynomial Equations}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {1}, number = {2}, pages = {207--220}, abstract = {

In this paper, first of all we give the necessary and sufficient conditions of the center of a class of planar quintic differential systems by using reflecting function method, and provide a simple proof of this results. Secondly, We use the reflecting integral to research the equivalence of the Abel equation and some complicated equations and derive their center conditions and discuss their integrability.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2019.207}, url = {http://global-sci.org/intro/article_detail/jnma/18858.html} }
TY - JOUR T1 - On the Integrability and Equivalence of the Abel Equation and Some Polynomial Equations AU - Yan , Yuexin AU - Pan , Yingxin AU - Lu , Feifei AU - Zhou , Zhengxin JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 207 EP - 220 PY - 2021 DA - 2021/04 SN - 1 DO - http://doi.org/10.12150/jnma.2019.207 UR - https://global-sci.org/intro/article_detail/jnma/18858.html KW - Center condition, integrability, reflecting integral, equivalence. AB -

In this paper, first of all we give the necessary and sufficient conditions of the center of a class of planar quintic differential systems by using reflecting function method, and provide a simple proof of this results. Secondly, We use the reflecting integral to research the equivalence of the Abel equation and some complicated equations and derive their center conditions and discuss their integrability.

Yan , YuexinPan , YingxinLu , Feifei and Zhou , Zhengxin. (2021). On the Integrability and Equivalence of the Abel Equation and Some Polynomial Equations. Journal of Nonlinear Modeling and Analysis. 1 (2). 207-220. doi:10.12150/jnma.2019.207
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