1. Applications of Solvable Lie Algebras to a Class of Third Order Equations.
- Author
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Bruzón, María S., de la Rosa, Rafael, Gandarias, María L., and Tracinà, Rita
- Subjects
- *
KORTEWEG-de Vries equation , *PARTIAL differential equations , *NONLINEAR differential equations , *EQUATIONS , *ELECTRIC lines , *LIE algebras , *SYMMETRY groups - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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