ANALYSIS OF SYMMETRIES, CONSERVATION LAWS, AND EXACT SOLUTIONS OF (1+ 1) REACTION-DIFFUSION EQUATION

Adnan Shamaoon*, Adeel Faruq

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Downloads (Pure)

Abstract

This research work provides an investigation of the (1+1) reaction-diffusion equation, which models population dynamics with spatially varying growth rates represented by z(x) using Lie point symmetries analysis. Our methodology involves categorising this equation into three distinct types based on the constraints imposed on the spatially dependent growth rate during the solution of the Lie group determining equations. For each category, we systematically derive the corresponding conservation laws associated with the identified symmetries. Additionally, we develop exact solutions for each type, offering a widespread understanding of the population dynamics modelled by the equation. We pay special attention to scale-invariant solutions, which are explored using the global invariants of the one-parameter group. This in-depth investigation not only enhances our theoretical understanding of reaction-diffusion processes in heterogeneous environments but also highlights the utility of symmetry methods in solving complex differential equations.
Original languageEnglish
Pages (from-to)7772-7783
Number of pages12
JournalInternational Journal of Science Academic Research
Volume05
Issue number07
Publication statusPublished - 19 Jul 2024

Keywords

  • Lie point symmetries
  • conservation laws
  • self-adjointness
  • exact solutions
  • invariant solutions
  • travelling wave solutions

Cite this