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Analysis of a Reaction–Diffusion–Advection Model with Various Allee Effects

Author

Listed:
  • Lewa’ Alzaleq

    (Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq 25113, Jordan)

  • Valipuram Manoranjan

    (Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA)

Abstract

This paper presents an extensive study of traveling wave solutions for a population model where the growth function incorporates the Allee effect. We are able to find closed form solutions for solitary waves that are kinks and pulses (bell type). Additionally, for every solution that we find, we show the corresponding phase portrait. Interestingly, we discover that, under certain conditions, standing waves of the bell and kink types exist too.

Suggested Citation

  • Lewa’ Alzaleq & Valipuram Manoranjan, 2023. "Analysis of a Reaction–Diffusion–Advection Model with Various Allee Effects," Mathematics, MDPI, vol. 11(10), pages 1-21, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2373-:d:1151366
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    References listed on IDEAS

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    1. Zheng, Bailin & Kai, Yue & Xu, Wenlong & Yang, Nan & Zhang, Kai & Thibado, P.M., 2019. "Exact traveling and non-traveling wave solutions of the time fractional reaction–diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 532(C).
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