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Optimal subalgebras and conservation laws with exact solutions for biological population model

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  • Shagolshem, Sumanta
  • Bira, B.
  • Zeidan, D.

Abstract

In the present study, we focus on the (2+1) dimensional normal biological population model (NBPM), which describes the population migration of species. We employ Lie symmetry analysis to the given nonlinear degenerate parabolic partial differential equation (PDE), which shows substantial advancement and upgraded results over other analytical techniques in determining some classes of exact solutions. Using the symmetry group of transformations, we construct the one-dimensional and two-dimensional optimal subalgebras for the NBPM. Further, we present the reduced ordinary differential equation(ODE) for each one-dimensional optimal subalgebras and construct some exact solutions for the physical model. Furthermore, we illustrate the physical behaviour of the model graphically through the obtained exact solutions. Lastly, applying the multipliers method, we develop some new conservation laws yielding some potential systems which are nonlocally related to the given PDE.

Suggested Citation

  • Shagolshem, Sumanta & Bira, B. & Zeidan, D., 2023. "Optimal subalgebras and conservation laws with exact solutions for biological population model," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s096007792201164x
    DOI: 10.1016/j.chaos.2022.112985
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    References listed on IDEAS

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    1. Sil, Subhankar & Raja Sekhar, T. & Zeidan, Dia, 2020. "Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Satapathy, Purnima & Raja Sekhar, T., 2018. "Optimal system, invariant solutions and evolution of weak discontinuity for isentropic drift flux model," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 107-116.
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