IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i18p3897-d1239138.html
   My bibliography  Save this article

Integration of Differential Equations by C ∞ -Structures

Author

Listed:
  • Antonio Jesús Pan-Collantes

    (Departamento de Matemáticas, IES San Juan de Dios, 11170 Medina Sidonia, Cádiz, Spain)

  • Concepción Muriel

    (Departamento de Matemáticas, Universidad de Cádiz, 11510 Puerto Real, Cádiz, Spain)

  • Adrián Ruiz

    (Departamento de Matemáticas, Universidad de Cádiz, 11510 Puerto Real, Cádiz, Spain)

Abstract

Several integrability problems of differential equations are addressed using the concept of a C ∞ -structure, a recent generalization of the notion of solvable structure. Specifically, the integration procedure associated with C ∞ -structures is used to integrate a Lotka–Volterra model and several differential equations that lack sufficient Lie point symmetries and cannot be solved using conventional methods.

Suggested Citation

  • Antonio Jesús Pan-Collantes & Concepción Muriel & Adrián Ruiz, 2023. "Integration of Differential Equations by C ∞ -Structures," Mathematics, MDPI, vol. 11(18), pages 1-23, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3897-:d:1239138
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/18/3897/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/18/3897/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mehdi Nadjafikhah & Saeed Dodangeh & Parastoo Kabi-Nejad, 2013. "On the Variational Problems without Having Desired Variational Symmetries," Journal of Mathematics, Hindawi, vol. 2013, pages 1-4, June.
    2. Mendoza, J. & Muriel, C., 2021. "New exact solutions for a generalised Burgers-Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Grammaticos, B. & Moulin-Ollagnier, J. & Ramani, A. & Strelcyn, J.-M. & Wojciechowski, S., 1990. "Integrals of quadratic ordinary differential equations in R3: The Lotka-Volterra system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 163(2), pages 683-722.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Figueiredo, A. & Filho, T.M.Rocha & Brenig, L., 1999. "Necessary conditions for the existence of quasi-polynomial invariants: the quasi-polynomial and Lotka–Volterra systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 262(1), pages 158-180.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3897-:d:1239138. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.