Lie symmetries and exact solutions for a fourth-order nonlinear diffusion equation

Identificadores
URI: http://hdl.handle.net/10498/26982
DOI: 10.1002/mma.8387
ISSN: 0170-4214
ISSN: 1099-1476
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2022-06Department
MatemáticasSource
Math Meth Appl Sci. 2022;1–14.Abstract
In this paper, we consider a fourth-order nonlinear diffusion partial differential
equation, depending on two arbitrary functions. First, we perform an analysis
of the symmetry reductions for this parabolic partial differential equation by
applying the Lie symmetry method. The invariance property of a partial differential
equation under a Lie group of transformations yields the infinitesimal
generators. By using this invariance condition, we present a complete classification
of the Lie point symmetries for the different forms of the functions that
the partial differential equation involves. Afterwards, the optimal systems of
one-dimensional subalgebras for each maximal Lie algebra are determined, by
computing previously the commutation relations, with the Lie bracket operator,
and the adjoint representation. Next, the reductions to ordinary differential
equations are derived from the optimal systems of one-dimensional subalgebras.
Furthermore, we study travelling wave reductions depending on the form of the
two arbitrary functions of the original equation. Some travelling wave solutions
are obtained, such as solitons, kinks and periodic waves.
Subjects
diffusion equations; exact solutions; Lie group analysis; symmetry reductionsCollections
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