%0 Journal Article 
%A Bruzón Gallego, María de los Santos
%A Rosa Silva, Rafael de la
%A Gandarias Núñez, María Luz
%A Tracinà, Rita
%T Applications of Solvable Lie Algebras to a Class of Third Order Equations
%D 2022
%@ 2227-7390
%U http://hdl.handle.net/10498/26504
%X 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.
%K third-order partial differential equations
%K lie symmetries
%K solvable symmetry algebras
%K group invariant solutions
%~ Universidad de Cádiz