Conservation laws for shallow water waves on a sloping beach
Shallow water waves are governed by a pair of non-linear partial differential equations. We transfer the associated homogeneous and non-homogeneous systems, (corresponding to constant and sloping depth, respectively), to the hodograph plane where we find all the non-simple wave solutions and constru...
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Hindawi Limited
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171286000480 |
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doaj-7e035a8818fc4d58ad393a98f999df492020-11-24T22:08:34ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019238739610.1155/S0161171286000480Conservation laws for shallow water waves on a sloping beachYilmaz Akyildiz0Department of Mathematical Sciences, University of Petroleum and Minerals, Dhahran, Saudi ArabiaShallow water waves are governed by a pair of non-linear partial differential equations. We transfer the associated homogeneous and non-homogeneous systems, (corresponding to constant and sloping depth, respectively), to the hodograph plane where we find all the non-simple wave solutions and construct infinitely many polynomial conservation laws. We also establish correspondence between conservation laws and hodograph solutions as well as Bäcklund transformations by using the linear nature of the problems on the hodogrpah plane.http://dx.doi.org/10.1155/S0161171286000480water wavesconservation lawsBäcklund transformation. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yilmaz Akyildiz |
| spellingShingle |
Yilmaz Akyildiz Conservation laws for shallow water waves on a sloping beach International Journal of Mathematics and Mathematical Sciences water waves conservation laws Bäcklund transformation. |
| author_facet |
Yilmaz Akyildiz |
| author_sort |
Yilmaz Akyildiz |
| title |
Conservation laws for shallow water waves on a sloping beach |
| title_short |
Conservation laws for shallow water waves on a sloping beach |
| title_full |
Conservation laws for shallow water waves on a sloping beach |
| title_fullStr |
Conservation laws for shallow water waves on a sloping beach |
| title_full_unstemmed |
Conservation laws for shallow water waves on a sloping beach |
| title_sort |
conservation laws for shallow water waves on a sloping beach |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1986-01-01 |
| description |
Shallow water waves are governed by a pair of non-linear partial differential equations. We transfer the associated homogeneous and non-homogeneous systems, (corresponding to constant and sloping depth, respectively), to the hodograph plane where we find all the non-simple wave solutions and construct infinitely many polynomial conservation laws. We also establish correspondence between conservation laws and hodograph solutions as well as Bäcklund transformations by using the linear nature of the problems on the hodogrpah plane. |
| topic |
water waves conservation laws Bäcklund transformation. |
| url |
http://dx.doi.org/10.1155/S0161171286000480 |
| work_keys_str_mv |
AT yilmazakyildiz conservationlawsforshallowwaterwavesonaslopingbeach |
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1725815920041918464 |