RT journal article
T1 Lie symmetries and exact solutions for a fourth-order nonlinear diffusion equation
A1 Márquez Lozano, Almudena del Pilar
A1 Garrido Letrán, Tamara María
A1 Recio Rodríguez, Elena
A1 Rosa Silva, Rafael de la
A2 Matemáticas
K1 diffusion equations
K1 exact solutions
K1 Lie group analysis
K1 symmetry reductions
AB In this paper, we consider a fourth-order nonlinear diffusion partial differentialequation, depending on two arbitrary functions. First, we perform an analysisof the symmetry reductions for this parabolic partial differential equation byapplying the Lie symmetry method. The invariance property of a partial differentialequation under a Lie group of transformations yields the infinitesimalgenerators. By using this invariance condition, we present a complete classificationof the Lie point symmetries for the different forms of the functions thatthe partial differential equation involves. Afterwards, the optimal systems ofone-dimensional subalgebras for each maximal Lie algebra are determined, bycomputing previously the commutation relations, with the Lie bracket operator,and the adjoint representation. Next, the reductions to ordinary differentialequations are derived from the optimal systems of one-dimensional subalgebras.Furthermore, we study travelling wave reductions depending on the form of thetwo arbitrary functions of the original equation. Some travelling wave solutionsare obtained, such as solitons, kinks and periodic waves.
PB WILEY
SN 0170-4214
YR 2022
FD 2022-06
LK http://hdl.handle.net/10498/26982
UL http://hdl.handle.net/10498/26982
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 21-sep-2026