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Reductions and Conservation Laws of a Generalized Third-Order PDE via Multi-Reduction Method

Author

Listed:
  • María S. Bruzón

    (Departamento de Matemáticas, Universidad de Cádiz, 11510 Puerto Real, Spain
    M.S.B. sadly passed away prior to the submission of this paper. This is one of her last works.)

  • Rafael de la Rosa

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

  • María L. Gandarias

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

  • Rita Tracinà

    (Dipartimento di Matematica e Informatica, Università di Catania, 95125 Catania, Italy)

Abstract

In this work, we consider a family of nonlinear third-order evolution equations, where two arbitrary functions depending on the dependent variable appear. Evolution equations of this type model several real-world phenomena, such as diffusion, convection, or dispersion processes, only to cite a few. By using the multiplier method, we compute conservation laws. Looking for traveling waves solutions, all the the conservation laws that are invariant under translation symmetries are directly obtained. Moreover, each of them will be inherited by the corresponding traveling wave ODEs, and a set of first integrals are obtained, allowing to reduce the nonlinear third-order evolution equations under consideration into a first-order autonomous equation.

Suggested Citation

  • María S. Bruzón & Rafael de la Rosa & María L. Gandarias & Rita Tracinà, 2022. "Reductions and Conservation Laws of a Generalized Third-Order PDE via Multi-Reduction Method," Mathematics, MDPI, vol. 10(6), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:954-:d:772979
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    References listed on IDEAS

    as
    1. Qiao, Zhijun & Liu, Liping, 2009. "A new integrable equation with no smooth solitons," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 587-593.
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    Cited by:

    1. Iqbal, Anjum & Naeem, Imran, 2022. "Exact solutions of a quintic dispersive equation," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

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