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Explicit series solution of travelling waves with a front of Fisher equation

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  • Tan, Yue
  • Xu, Hang
  • Liao, Shi-Jun

Abstract

In this paper, an analytic technique, namely the homotopy analysis method, is employed to solve the Fisher equation, which describes a family of travelling waves with a front. The explicit series solution for all possible wave speeds 0

Suggested Citation

  • Tan, Yue & Xu, Hang & Liao, Shi-Jun, 2007. "Explicit series solution of travelling waves with a front of Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 462-472.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:2:p:462-472
    DOI: 10.1016/j.chaos.2005.10.001
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    Citations

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    Cited by:

    1. Abbasbandy, S. & Parkes, E.J., 2008. "Solitary smooth hump solutions of the Camassa–Holm equation by means of the homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 581-591.
    2. Abbasbandy, S., 2009. "Solitary wave solutions to the modified form of Camassa–Holm equation by means of the homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 428-435.
    3. Deng, Dingwen & Xiong, Xiaohong, 2024. "Explicit, non-negativity-preserving and maximum-principle-satisfying finite difference scheme for the nonlinear Fisher's equation," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    4. Cveticanin, L., 2009. "Application of homotopy-perturbation to non-linear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 221-228.
    5. Hayat, T. & Abbas, Z. & Javed, T. & Sajid, M., 2009. "Three-dimensional rotating flow induced by a shrinking sheet for suction," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1615-1626.
    6. Sajid, M. & Hayat, T., 2008. "The application of homotopy analysis method to thin film flows of a third order fluid," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 506-515.
    7. Allan, Fathi M., 2009. "Construction of analytic solution to chaotic dynamical systems using the Homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1744-1752.
    8. Hayat, T. & Abbas, Z., 2008. "Heat transfer analysis on the MHD flow of a second grade fluid in a channel with porous medium," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 556-567.
    9. 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.

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