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Lie symmetries and travelling wave solutions of the nonlinear waves in the inhomogeneous Fisher‐Kolmogorov equation
Author(s) -
Bruzón M.S.,
Garrido T.M.,
Recio E.,
Rosa R.
Publication year - 2019
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.5977
Subject(s) - mathematics , fisher's equation , partial differential equation , first order partial differential equation , mathematical analysis , fisher equation , ordinary differential equation , homogeneous space , differential equation , exponential function , nonlinear system , kadomtsev–petviashvili equation , symmetry (geometry) , exact differential equation , burgers' equation , geometry , physics , real interest rate , quantum mechanics , monetary economics , economics , interest rate
In this work, we consider a Fisher‐Kolmogorov equation depending on two exponential functions of the spatial variables. We study this equation from the point of view of symmetry reductions in partial differential equations. Through two‐dimensional abelian subalgebras, the equation is reduced to ordinary differential equations. New solutions have been derived and interpreted.