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Exact smooth and sharp-fronted travelling waves of reaction–diffusion equations with Weak Allee effects

Fadai, Nabil T

Authors

NABIL FADAI NABIL.FADAI@NOTTINGHAM.AC.UK
Assistant Professor



Abstract

We provide new exact forms of smooth and sharp-fronted travelling wave solutions of the reaction–diffusion equation, ∂tu=R(u)+∂xD(u)∂xu, where the reaction term, R(u), employs a Weak Allee effect. The resulting ordinary differential equation system is solved by means of constructing a power series solution of the heteroclinic trajectory in phase plane space. For specific choices of wavespeeds and standard Weak Allee reaction terms, extending the celebrated exact travelling wave solution of the FKPP equation with wavespeed 5/6, we determine a family of exact travelling wave solutions that are smooth or sharp-fronted.

Citation

Fadai, N. T. (2023). Exact smooth and sharp-fronted travelling waves of reaction–diffusion equations with Weak Allee effects. Applied Mathematics Letters, 135, Article 108433. https://doi.org/10.1016/j.aml.2022.108433

Journal Article Type Article
Acceptance Date Aug 30, 2022
Online Publication Date Sep 17, 2022
Publication Date Jan 1, 2023
Deposit Date Sep 1, 2022
Publicly Available Date Sep 21, 2022
Journal Applied Mathematics Letters
Print ISSN 0893-9659
Electronic ISSN 1873-5452
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 135
Article Number 108433
DOI https://doi.org/10.1016/j.aml.2022.108433
Keywords Fisher's equation; nonlinear diffusion; Stefan condition; moving boundary problem
Public URL https://nottingham-repository.worktribe.com/output/10634878
Publisher URL https://www.sciencedirect.com/science/article/pii/S0893965922002968

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