RT journal article
T1 Applications of Solvable Lie Algebras to a Class of Third Order Equations
A1 Bruzón Gallego, María de los Santos
A1 Rosa Silva, Rafael de la
A1 Gandarias Núñez, María Luz
A1 Tracinà, Rita
A2 Matemáticas
K1 third-order partial differential equations
K1 lie symmetries
K1 solvable symmetry algebras
K1 group invariant solutions
AB A family of third-order partial differential equations (PDEs) is analyzed. This familybroadens out well-known PDEs such as the Korteweg-de Vries equation, the Gardner equation, andthe Burgers equation, which model many real-world phenomena. Furthermore, several macroscopicmodels for semiconductors considering quantum effects—for example, models for the transmission ofelectrical 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 determinegroup-invariant solutions from three-dimensional solvable subgroups of the complete symmetrygroup, 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 takinginto account the Type-II hidden symmetries that appear in the reduced second-order ODEs.
PB MDPI
SN 2227-7390
YR 2022
FD 2022-01
LK http://hdl.handle.net/10498/26504
UL http://hdl.handle.net/10498/26504
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 21-sep-2026