@misc{10498/26504,
year = {2022},
month = {1},
url = {http://hdl.handle.net/10498/26504},
abstract = {A family of third-order partial differential equations (PDEs) is analyzed. This family
broadens out well-known PDEs such as the Korteweg-de Vries equation, the Gardner equation, and
the Burgers equation, which model many real-world phenomena. Furthermore, several macroscopic
models for semiconductors considering quantum effects—for example, models for the transmission of
electrical lines and quantum hydrodynamic models—are governed by third-order PDEs of this family.
For this family, all point symmetries have been derived. These symmetries are used to determine
group-invariant solutions from three-dimensional solvable subgroups of the complete symmetry
group, which allow us to reduce the given PDE to a first-order nonlinear ordinary differential equation
(ODE). Finally, exact solutions are obtained by solving the first-order nonlinear ODEs or by taking
into account the Type-II hidden symmetries that appear in the reduced second-order ODEs.},
publisher = {MDPI},
keywords = {third-order partial differential equations},
keywords = {lie symmetries},
keywords = {solvable symmetry algebras},
keywords = {group invariant solutions},
title = {Applications of Solvable Lie Algebras to a Class of Third Order Equations},
doi = {10.3390/math10020254},
author = {Bruzón Gallego, María de los Santos and Rosa Silva, Rafael de la and Gandarias Núñez, María Luz and Tracinà, Rita},
}