Three-dimensional Korteweg-de Vries equation and traveling wave solutions
The three-dimensional power Korteweg-de Vries equation [ut+unux+uxxx]x+uyy+uzz=0, is considered. Solitary wave solutions for any positive integer n and cnoidal wave solutions for n=1 and n=2 are obtained. The cnoidal wave solutions are shown to be represented as infinite sums of solitons by using F...
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171200004440 |
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| _version_ | 1832556575034703872 |
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| author | Kenneth L. Jones |
| author_facet | Kenneth L. Jones |
| author_sort | Kenneth L. Jones |
| collection | DOAJ |
| description | The three-dimensional power Korteweg-de Vries equation
[ut+unux+uxxx]x+uyy+uzz=0, is
considered. Solitary wave solutions for any positive integer n and cnoidal wave solutions for n=1 and n=2 are obtained. The
cnoidal wave solutions are shown to be represented as infinite sums
of solitons by using Fourier series expansions and Poisson's
summation formula. |
| format | Article |
| id | doaj-art-d9c8158b2afc4a8f8963863405a49499 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d9c8158b2afc4a8f8963863405a494992025-02-03T05:44:59ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-0124637938410.1155/S0161171200004440Three-dimensional Korteweg-de Vries equation and traveling wave solutionsKenneth L. Jones0Department of Mathematics and Computer Science, Fayetteville State University, Fayetteville 28301-4298, North Carolina, USAThe three-dimensional power Korteweg-de Vries equation [ut+unux+uxxx]x+uyy+uzz=0, is considered. Solitary wave solutions for any positive integer n and cnoidal wave solutions for n=1 and n=2 are obtained. The cnoidal wave solutions are shown to be represented as infinite sums of solitons by using Fourier series expansions and Poisson's summation formula.http://dx.doi.org/10.1155/S0161171200004440Korteweg-de Vries equationtraveling wave solutions. |
| spellingShingle | Kenneth L. Jones Three-dimensional Korteweg-de Vries equation and traveling wave solutions International Journal of Mathematics and Mathematical Sciences Korteweg-de Vries equation traveling wave solutions. |
| title | Three-dimensional Korteweg-de Vries equation and traveling wave solutions |
| title_full | Three-dimensional Korteweg-de Vries equation and traveling wave solutions |
| title_fullStr | Three-dimensional Korteweg-de Vries equation and traveling wave solutions |
| title_full_unstemmed | Three-dimensional Korteweg-de Vries equation and traveling wave solutions |
| title_short | Three-dimensional Korteweg-de Vries equation and traveling wave solutions |
| title_sort | three dimensional korteweg de vries equation and traveling wave solutions |
| topic | Korteweg-de Vries equation traveling wave solutions. |
| url | http://dx.doi.org/10.1155/S0161171200004440 |
| work_keys_str_mv | AT kennethljones threedimensionalkortewegdevriesequationandtravelingwavesolutions |