IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v329y2018icp278-296.html
   My bibliography  Save this article

Riccati–Ermakov systems and explicit solutions for variable coefficient reaction–diffusion equations

Author

Listed:
  • Pereira, Enrique
  • Suazo, Erwin
  • Trespalacios, Jessica

Abstract

We present several families of nonlinear reaction–diffusion equations with variable coefficients including generalizations of Fisher–KPP and Burgers type equations. Special exact solutions such as traveling wave, rational, triangular wave and N-wave type solutions are shown. By means of similarity transformations the variable coefficients are conditioned to satisfy Riccati or Ermakov systems of equations. When the Riccati system is used, conditions are established so that finite-time singularities might occur. We explore solution dynamics across multi-parameters. In the supplementary material, we provide a computer algebra verification of the solutions and exemplify nontrivial dynamics of the solutions.

Suggested Citation

  • Pereira, Enrique & Suazo, Erwin & Trespalacios, Jessica, 2018. "Riccati–Ermakov systems and explicit solutions for variable coefficient reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 278-296.
    • Handle: RePEc:eee:apmaco:v:329:y:2018:i:c:p:278-296
    DOI: 10.1016/j.amc.2018.01.047
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318300705
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.01.047?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zola, R.S. & Dias, J.C. & Lenzi, E.K. & Evangelista, L.R. & Lenzi, M.K. & da Silva, L.R., 2008. "Exact solutions for a forced Burgers equation with a linear external force," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2690-2696.
    2. Feng, Zhaosheng, 2008. "Traveling wave behavior for a generalized fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 481-488.
    3. Escorcia, J. & Suazo, E., 2017. "Blow-up results and soliton solutions for a generalized variable coefficient nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 155-176.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. José M. Escorcia & Erwin Suazo, 2024. "On Blow-Up and Explicit Soliton Solutions for Coupled Variable Coefficient Nonlinear Schrödinger Equations," Mathematics, MDPI, vol. 12(17), pages 1-21, August.
    2. Polyanin, Andrei D., 2019. "Functional separable solutions of nonlinear reaction–diffusion equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 282-292.

    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. Wu, Shi-Liang & Li, Wan-Tong, 2009. "Global asymptotic stability of bistable traveling fronts in reaction-diffusion systems and their applications to biological models," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1229-1239.
    2. Guo, Gang & Li, Kun & Wang, Yuhui, 2015. "Exact solutions of a modified fractional diffusion equation in the finite and semi-infinite domains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 193-201.
    3. Oraby, T. & Suazo, E. & Arrubla, H., 2023. "Probabilistic solutions of fractional differential and partial differential equations and their Monte Carlo simulations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

    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:eee:apmaco:v:329:y:2018:i:c:p:278-296. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.