On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations
We carry out a classification of Lie symmetries for the (2+1)-dimensional nonlinear damped wave equation utt+fuut=div(gugrad u) with variable damping. Similarity reductions of the equation are performed using the admitted Lie symmetries of the equation and some interesting solutions are presented. E...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/9401205 |
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| _version_ | 1832558874261979136 |
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| author | Usamah S. Al-Ali Ashfaque H. Bokhari A. H. Kara F. D. Zaman |
| author_facet | Usamah S. Al-Ali Ashfaque H. Bokhari A. H. Kara F. D. Zaman |
| author_sort | Usamah S. Al-Ali |
| collection | DOAJ |
| description | We carry out a classification of Lie symmetries for the (2+1)-dimensional nonlinear damped wave equation utt+fuut=div(gugrad u) with variable damping. Similarity reductions of the equation are performed using the admitted Lie symmetries of the equation and some interesting solutions are presented. Employing the multiplier approach, admitted conservation laws of the equation are constructed for some new, interesting cases. |
| format | Article |
| id | doaj-art-808b0a81c7cc4527b6379b90a18b21be |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-808b0a81c7cc4527b6379b90a18b21be2025-02-03T01:31:21ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/94012059401205On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave EquationsUsamah S. Al-Ali0Ashfaque H. Bokhari1A. H. Kara2F. D. Zaman3Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaDepartment of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaSchool of Mathematics, University of the Witwatersrand, Johannesburg, Wits 2050, South AfricaDepartment of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaWe carry out a classification of Lie symmetries for the (2+1)-dimensional nonlinear damped wave equation utt+fuut=div(gugrad u) with variable damping. Similarity reductions of the equation are performed using the admitted Lie symmetries of the equation and some interesting solutions are presented. Employing the multiplier approach, admitted conservation laws of the equation are constructed for some new, interesting cases.http://dx.doi.org/10.1155/2017/9401205 |
| spellingShingle | Usamah S. Al-Ali Ashfaque H. Bokhari A. H. Kara F. D. Zaman On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations Advances in Mathematical Physics |
| title | On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations |
| title_full | On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations |
| title_fullStr | On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations |
| title_full_unstemmed | On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations |
| title_short | On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations |
| title_sort | on the symmetries and conservation laws of the multidimensional nonlinear damped wave equations |
| url | http://dx.doi.org/10.1155/2017/9401205 |
| work_keys_str_mv | AT usamahsalali onthesymmetriesandconservationlawsofthemultidimensionalnonlineardampedwaveequations AT ashfaquehbokhari onthesymmetriesandconservationlawsofthemultidimensionalnonlineardampedwaveequations AT ahkara onthesymmetriesandconservationlawsofthemultidimensionalnonlineardampedwaveequations AT fdzaman onthesymmetriesandconservationlawsofthemultidimensionalnonlineardampedwaveequations |