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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.