IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v290y2016icp33-45.html
   My bibliography  Save this article

The effect of perturbed advection on a class of solutions of a non-linear reaction-diffusion equation

Author

Listed:
  • Varatharajan, N.
  • DasGupta, Anirvan

Abstract

In this work, the traveling wave solutions of a one-dimensional reaction-diffusion equation with advection are studied. The traveling wave solutions are obtained using the G′/G-expansion method. The shock thickness and spectral stability have been discussed for the obtained solution in the parameter interval. The essential spectra of the perturbed and linearized differential operator about the traveling antikink and kink solutions at the equilibrium states are obtained. The point spectrum is calculated using Evans function with Lie midpoint method and Magnus method. It is shown that, for a symmetric potential well, the traveling kink and antikink solutions which connect the stable equilibrium states of the system are stable. It is observed that the perturbation on the advection exhibits contrasting effect on the solution properties (shock thickness and the eigenvalue) of kink and antikink solutions. Variation of the reaction coefficient leads to instability of the solutions, unlike the diffusion coefficient which enhances the stability. On the other hand, the variation of reaction and diffusion coefficients show the monotonic effect on the shock thickness of the traveling kink and antikink solutions. This study is expected to be useful in analyzing the slow or fast invasion and stability of the population movement in different steady states.

Suggested Citation

  • Varatharajan, N. & DasGupta, Anirvan, 2016. "The effect of perturbed advection on a class of solutions of a non-linear reaction-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 33-45.
    • Handle: RePEc:eee:apmaco:v:290:y:2016:i:c:p:33-45
    DOI: 10.1016/j.amc.2016.05.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316303460
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.05.037?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. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    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. Yu, Hao & Wu, Boying & Zhang, Dazhi, 2018. "A generalized Laguerre spectral Petrov–Galerkin method for the time-fractional subdiffusion equation on the semi-infinite domain," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 96-111.

    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. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
    2. Sheng Zhang & Jiao Gao & Bo Xu, 2022. "An Integrable Evolution System and Its Analytical Solutions with the Help of Mixed Spectral AKNS Matrix Problem," Mathematics, MDPI, vol. 10(21), pages 1-16, October.
    3. Xu, Lan, 2008. "Variational approach to solitons of nonlinear dispersive K(m,n) equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 137-143.
    4. Suheel Abdullah Malik & Ijaz Mansoor Qureshi & Muhammad Amir & Aqdas Naveed Malik & Ihsanul Haq, 2015. "Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-15, March.
    5. Zeng, Xiping & Dai, Zhengde & Li, Donglong, 2009. "New periodic soliton solutions for the (3+1)-dimensional potential-YTSF equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 657-661.
    6. Nguyen, Lu Trong Khiem, 2015. "Modified homogeneous balance method: Applications and new solutions," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 148-155.
    7. M. Ali Akbar & Md. Nur Alam & Md. Golam Hafez, 2016. "Application of the novel (G′/G)-expansion method to construct traveling wave solutions to the positive Gardner-KP equation," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(1), pages 85-96, March.
    8. Javidi, M. & Golbabai, A., 2009. "Modified homotopy perturbation method for solving non-linear Fredholm integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1408-1412.
    9. Oke Davies Adeyemo & Lijun Zhang & Chaudry Masood Khalique, 2022. "Bifurcation Theory, Lie Group-Invariant Solutions of Subalgebras and Conservation Laws of a Generalized (2+1)-Dimensional BK Equation Type II in Plasma Physics and Fluid Mechanics," Mathematics, MDPI, vol. 10(14), pages 1-46, July.
    10. Hussain, Akhtar & Ibrahim, Tarek F. & Birkea, Fathea M.O. & Al-Sinan, B.R. & Alotaibi, Abeer M., 2024. "Abundant analytical solutions and diverse solitonic patterns for the complex Ginzburg–Landau equation," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    11. Jing Chang & Jin Zhang & Ming Cai, 2021. "Series Solutions of High-Dimensional Fractional Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-21, August.
    12. EL Achab, Abdelfattah, 2020. "On the integrability of the generalized Pochhammer–Chree (PC) equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    13. Akbar, Yasir & Afsar, Haleem & Abbas, Shahzad & Javed, Muhammad Waqas & Ullah, Najib, 2021. "Dromions for the coupled Maccari’s system in fluid mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    14. Bekir, Ahmet & Cevikel, Adem C., 2009. "New exact travelling wave solutions of nonlinear physical models," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1733-1739.
    15. Sheng Zhang & Lijie Zhang & Bo Xu, 2019. "Rational Waves and Complex Dynamics: Analytical Insights into a Generalized Nonlinear Schrödinger Equation with Distributed Coefficients," Complexity, Hindawi, vol. 2019, pages 1-17, March.
    16. Tariq, Kalim U. & Bekir, Ahmet & Nisar, Sana, 2023. "The dynamical structures of the Sharma–Tasso–Olver model in doubly dispersive medium," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    17. Zhou, Jiangrui & Zhou, Rui & Zhu, Shihui, 2020. "Peakon, rational function and periodic solutions for Tzitzeica–Dodd–Bullough type equations," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    18. Golbabai, A. & Javidi, M., 2009. "A spectral domain decomposition approach for the generalized Burger’s–Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 385-392.
    19. (Benn)Wu, Xu-Hong & He, Ji-Huan, 2008. "EXP-function method and its application to nonlinear equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 903-910.
    20. Abdel-Gawad, Hamdy I. & Abdel-Gawad, Ahmed H., 2021. "Discrete and continuum models of COVID-19 virus, formal solutions, stability and comparison with real data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 222-230.

    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:290:y:2016:i:c:p:33-45. 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.