The shallow water equations: conservation laws and symplectic geometry
We consider the system of nonlinear differential equations governing shallow water waves over a uniform or sloping bottom. By using the hodograph method we construct solutions, conservation laws, and Böcklund transformations for these equations. We show that these constructions are canonical relativ...
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| Format: | Article |
| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117128700067X |
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| _version_ | 1832559351235084288 |
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| author | Yilmaz Akyildiz |
| author_facet | Yilmaz Akyildiz |
| author_sort | Yilmaz Akyildiz |
| collection | DOAJ |
| description | We consider the system of nonlinear differential equations governing shallow
water waves over a uniform or sloping bottom. By using the hodograph method we construct solutions, conservation laws, and Böcklund transformations for these equations. We show that these constructions are canonical relative to a symplectic form introduced by Manin. |
| format | Article |
| id | doaj-art-67035970ab3740ca966de4bf373ce12a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-67035970ab3740ca966de4bf373ce12a2025-02-03T01:30:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110355756210.1155/S016117128700067XThe shallow water equations: conservation laws and symplectic geometryYilmaz Akyildiz0Department of Mathematical Sciences, University of Petroleum and Minerals, Dhahran 31261, Saudi ArabiaWe consider the system of nonlinear differential equations governing shallow water waves over a uniform or sloping bottom. By using the hodograph method we construct solutions, conservation laws, and Böcklund transformations for these equations. We show that these constructions are canonical relative to a symplectic form introduced by Manin.http://dx.doi.org/10.1155/S016117128700067Xshallow water waveshodograph transformationsimple-waveBöcklund transformationHamiltonian formalismsymplecticcompletely integrable system. |
| spellingShingle | Yilmaz Akyildiz The shallow water equations: conservation laws and symplectic geometry International Journal of Mathematics and Mathematical Sciences shallow water waves hodograph transformation simple-wave Böcklund transformation Hamiltonian formalism symplectic completely integrable system. |
| title | The shallow water equations: conservation laws and symplectic geometry |
| title_full | The shallow water equations: conservation laws and symplectic geometry |
| title_fullStr | The shallow water equations: conservation laws and symplectic geometry |
| title_full_unstemmed | The shallow water equations: conservation laws and symplectic geometry |
| title_short | The shallow water equations: conservation laws and symplectic geometry |
| title_sort | shallow water equations conservation laws and symplectic geometry |
| topic | shallow water waves hodograph transformation simple-wave Böcklund transformation Hamiltonian formalism symplectic completely integrable system. |
| url | http://dx.doi.org/10.1155/S016117128700067X |
| work_keys_str_mv | AT yilmazakyildiz theshallowwaterequationsconservationlawsandsymplecticgeometry AT yilmazakyildiz shallowwaterequationsconservationlawsandsymplecticgeometry |