Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave Equation
This paper studies a non-linear viscoelastic wave equation, with non-linear damping and source terms, from the point of view of the Lie groups theory. Firstly, we apply Lie’s symmetries method to the partial differential equation to classify the Lie point symmetries. Afterwards, we reduce the partia...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/17/2131 |
| _version_ | 1797521092783374336 |
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| author | Almudena P. Márquez María S. Bruzón |
| author_facet | Almudena P. Márquez María S. Bruzón |
| author_sort | Almudena P. Márquez |
| collection | DOAJ |
| description | This paper studies a non-linear viscoelastic wave equation, with non-linear damping and source terms, from the point of view of the Lie groups theory. Firstly, we apply Lie’s symmetries method to the partial differential equation to classify the Lie point symmetries. Afterwards, we reduce the partial differential equation to some ordinary differential equations, by using the symmetries. Therefore, new analytical solutions are found from the ordinary differential equations. Finally, we derive low-order conservation laws, depending on the form of the damping and source terms, and discuss their physical meaning. |
| first_indexed | 2024-03-10T08:06:46Z |
| format | Article |
| id | doaj.art-50c6924702c444dcaadf64e760b2304d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:06:46Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-50c6924702c444dcaadf64e760b2304d2023-11-22T10:58:23ZengMDPI AGMathematics2227-73902021-09-01917213110.3390/math9172131Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave EquationAlmudena P. Márquez0María S. Bruzón1Department of Mathematics, University of Cadiz, Puerto Real, 11510 Cadiz, SpainDepartment of Mathematics, University of Cadiz, Puerto Real, 11510 Cadiz, SpainThis paper studies a non-linear viscoelastic wave equation, with non-linear damping and source terms, from the point of view of the Lie groups theory. Firstly, we apply Lie’s symmetries method to the partial differential equation to classify the Lie point symmetries. Afterwards, we reduce the partial differential equation to some ordinary differential equations, by using the symmetries. Therefore, new analytical solutions are found from the ordinary differential equations. Finally, we derive low-order conservation laws, depending on the form of the damping and source terms, and discuss their physical meaning.https://www.mdpi.com/2227-7390/9/17/2131viscoelastic wave equationLie symmetriestraveling wave solutionsconversation laws |
| spellingShingle | Almudena P. Márquez María S. Bruzón Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave Equation Mathematics viscoelastic wave equation Lie symmetries traveling wave solutions conversation laws |
| title | Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave Equation |
| title_full | Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave Equation |
| title_fullStr | Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave Equation |
| title_full_unstemmed | Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave Equation |
| title_short | Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave Equation |
| title_sort | lie point symmetries traveling wave solutions and conservation laws of a non linear viscoelastic wave equation |
| topic | viscoelastic wave equation Lie symmetries traveling wave solutions conversation laws |
| url | https://www.mdpi.com/2227-7390/9/17/2131 |
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