| Autor: |
María S. Bruzón, Rafael de la Rosa, María L. Gandarias, Rita Tracinà |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Mathematics, Vol 10, Iss 2, p 254 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2227-7390 |
| DOI: |
10.3390/math10020254 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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