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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Mendoza, J. & Muriel, C., 2021. "New exact solutions for a generalised Burgers-Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
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