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Qualitative Properties of the Solutions to the Lane–Emden Equation in the Cylindrical Setup

Author

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  • Arsen Palestini

    (Dipartimento di Metodi e Modelli per l’Economia il Territorio e la Finanza MEMOTEF, Sapienza University of Rome, Via del Castro Laurenziano 9, 00161 Rome, Italy
    These authors contributed equally to this work.)

  • Simone Recchi

    (Independent Researcher, Urbangasse 6/3/41, 1170 Wien, Austria
    These authors contributed equally to this work.)

Abstract

We analyze the Lane–Emden equations in the cylindrical framework. Although the explicit forms of the solutions (which are also called polytropes) are not known, we identify some of their qualitative properties. In particular, possible critical points and zeros of the polytropes are investigated and discussed, leading to possible improvements in the approximation methods which are currently employed. The cases when the critical parameter is odd and even are separately analyzed. Furthermore, we propose a technique to evaluate the distance between a pair of polytropes in small intervals.

Suggested Citation

  • Arsen Palestini & Simone Recchi, 2024. "Qualitative Properties of the Solutions to the Lane–Emden Equation in the Cylindrical Setup," Mathematics, MDPI, vol. 12(4), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:542-:d:1336673
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    References listed on IDEAS

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    1. Swati, & Singh, Mandeep & Singh, Karanjeet, 2023. "An efficient technique based on higher order Haar wavelet method for Lane–Emden equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 21-39.
    2. Bengochea, Gabriel, 2014. "Algebraic approach to the Lane–Emden equation," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 424-430.
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