Geometric Solutions of a Quadratic Polynomial Differential System Having the First Integral

Ahlam Belfar; Rebiha Benterki; Halla Sellami

doi:10.2478/tmmp-2025-0024

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Geometric Solutions of a Quadratic Polynomial Differential System Having the First Integral

Tatra Mountains Mathematical Publications

Volume 90 (2025): Issue 2 (December 2025)

By: Ahlam Belfar, Rebiha Benterki and Halla Sellami

Open Access

|Dec 2025

Abstract

In this paper, we classify the geometric solutions of a class of integrable quadratic polynomial differential systems. We provide a new class of quadratic polynomial differential system that exhibits the so-called cubic egg curve as a first integral, we analyze the geometric solutions of this class in the Poincaré disc.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2025-0024 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 91 - 106

Submitted on: Feb 15, 2024

Accepted on: Feb 12, 2025

Published on: Dec 18, 2025

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

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© 2025 Ahlam Belfar, Rebiha Benterki, Halla Sellami, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 90 (2025): Issue 2 (December 2025)