Existence of Periodic Traveling Waves in the Klausmeier Model of Desertification and its Modification: A Comparative Study

Authors

  • Md AS Howlader Department of Mathematics, Jahangirnagar University, Savar
  • Md Ariful Islam Arif Department of Mathematics, Jahangirnagar University, Savar, Dhaka
  • LS Andallah Department of Mathematics, Jahangirnagar University, Savar, Dhaka
  • M Osman Gani Department of Mathematics, Jahangirnagar University, Savar, Dhaka

DOI:

https://doi.org/10.3329/ganit.v38i0.39783

Keywords:

Klausmeier model, periodic traveling waves, desertification, reaction-advection-diffusion equations.

Abstract

Self-organized and spatially periodic banded vegetation patterns have been observed in many semi-arid ecosystems. In order to understand the mechanism of these patterns, we consider a system of reaction-advection-diffusion equations in a two-variable model of desertification. This work deals with the investigation of the existence of periodic traveling waves in a one-parameter family of solutions. In addition, we investigate the existence of periodic traveling waves as a function of water transport parameter in the model.

GANIT J. Bangladesh Math. Soc.Vol. 38 (2018) 27-46

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Author Biographies

Md AS Howlader, Department of Mathematics, Jahangirnagar University, Savar

Department of Mathematics

Md Ariful Islam Arif, Department of Mathematics, Jahangirnagar University, Savar, Dhaka

Department of Mathematics

LS Andallah, Department of Mathematics, Jahangirnagar University, Savar, Dhaka

Department of Mathematics

M Osman Gani, Department of Mathematics, Jahangirnagar University, Savar, Dhaka

Department of Mathematics

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Published

2018-12-30

How to Cite

Howlader, M. A., Arif, M. A. I., Andallah, L., & Gani, M. O. (2018). Existence of Periodic Traveling Waves in the Klausmeier Model of Desertification and its Modification: A Comparative Study. GANIT: Journal of Bangladesh Mathematical Society, 38, 27–46. https://doi.org/10.3329/ganit.v38i0.39783

Issue

Vol. 38 (2018)

Section

Articles

License

The copyright of GANIT: Journal of Bangladesh Mathematical Society is reserved by Bangladesh Mathematical Society (web: https://bdmathsociety.org/)