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Symmetry analysis for a Fisher equation with exponential diffusion
Author(s) -
Gandarias M. L.,
Rosa M.,
Tracinà R.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4803
Subject(s) - mathematics , fisher equation , fisher's equation , partial differential equation , equivalence (formal languages) , differential equation , heat equation , symmetry (geometry) , exponential function , mathematical analysis , diffusion equation , reaction–diffusion system , first order partial differential equation , exact differential equation , pure mathematics , geometry , economy , real interest rate , monetary economics , economics , interest rate , service (business)
In this paper, we consider a generalized Fisher equation with exponential diffusion from the point of view of the theory of symmetry reductions in partial differential equations. The generalized Fisher‐type equation arises in the theory of population dynamics. These types of equations have appeared in many fields of study such as in the reaction‐diffusion equations, in heat transfer problems, in biology, and in chemical kinetics. By using the symmetry classification, simplified by equivalence transformations, for a special family of Fisher equations, all the reductions are derived from the optimal system of subalgebras and symmetry reductions are used to obtain exact solutions.