Exact time-dependent solutions of a Fisher–KPP-like equation obtained with nonclassical symmetry analysis. (October 2022)

• Record Type: Journal Article
• Authors: McCue, Scott W.; Bradshaw-Hajek, Bronwyn H.; Simpson, Matthew J.
• Is Part Of: Applied mathematics letters. Volume 132(2022)
• Publication Date: 2022-10
• Subjects: Fisher–Kolmogorov -- Nonclassical symmetry analysis -- Reaction–diffusion -- Population biology; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2022.108151
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We consider a family of exact solutions to a nonlinear reaction–diffusion model, constructed using nonclassical symmetry analysis. In a particular limit, the mathematical model approaches the well-known Fisher–KPP model, which means that it is related to various applications including cancer progression, wound healing and ecological invasion. The exact solution is mathematically interesting since exact solutions of the Fisher–KPP model are rare, and often restricted to long-time travelling wave solutions for special values of the travelling wave speed.