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Applications of Solvable Lie Algebras to a Class of Third Order Equations.
- Source :
- Mathematics (2227-7390); Jan2022, Vol. 10 Issue 2, p254-N.PAG, 1p
- Publication Year :
- 2022
-
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]
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 10
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 154854335
- Full Text :
- https://doi.org/10.3390/math10020254