Conservation laws, symmetries, and exact solutions of the classical Burgers–Fisher equation in two dimensions

This work investigates a spatially two-dimensional advection–diffusion–reaction equation that generalizes the Burgers’ and the Fisher’s equations, having the properties of convective phenomenon from Burgers equation as well as diffusion transport and reaction phenomena from Fisher’s equation. The tw...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2019-07, Vol.354, p.545-550
Main Authors: Rosa, M., Camacho, J.C., Bruzón, M.S., Gandarias, M.L.
Format: Article
Language:English
Subjects:
Burgers–Fisher equation
Lie symmetries
Partial differential equations
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Summary:This work investigates a spatially two-dimensional advection–diffusion–reaction equation that generalizes the Burgers’ and the Fisher’s equations, having the properties of convective phenomenon from Burgers equation as well as diffusion transport and reaction phenomena from Fisher’s equation. The two-dimensional equation is analysed from the point of view of the theory of symmetry reductions in partial differential equations. Conservation laws and exact solutions from double reductions are derived. Finally, an explicit shock wave solution is obtained.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2018.11.008