Nearly conconcentric Korteweg-de Vries equation and periodic traveling wave solution
The generalized nearly concentric Korteweg-de Vries equation [un+u/(2η)+u2uζ+uζζζ]ζ+uθθ/η2=0 is considered. The author converts the equation into the power Kadomtsev-Petviashvili equation [ut+unux+uxxx]x+uyy=0. Solitary wave solutions and cnoidal wave solutions are obtained. The cnoidal wave soluti...
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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171298000246 |
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| _version_ | 1849684038387761152 |
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| author | Yunkai Chen |
| author_facet | Yunkai Chen |
| author_sort | Yunkai Chen |
| collection | DOAJ |
| description | The generalized nearly concentric Korteweg-de Vries equation [un+u/(2η)+u2uζ+uζζζ]ζ+uθθ/η2=0 is considered. The author converts the equation into the power Kadomtsev-Petviashvili equation
[ut+unux+uxxx]x+uyy=0. Solitary wave solutions and cnoidal wave solutions are
obtained. The cnoidal wave solutions are shown to be representable as infinite sums of solitons by using
Fourier series expansions and Poisson's summation formula. |
| format | Article |
| id | doaj-art-cbc252098dca42b5a115ed5e6147a22c |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cbc252098dca42b5a115ed5e6147a22c2025-08-20T03:23:35ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121118318710.1155/S0161171298000246Nearly conconcentric Korteweg-de Vries equation and periodic traveling wave solutionYunkai Chen0Department of Mathematics and Computer Science, Fayetteville State University, Fayetteville 28301-4298, North Carolina, USAThe generalized nearly concentric Korteweg-de Vries equation [un+u/(2η)+u2uζ+uζζζ]ζ+uθθ/η2=0 is considered. The author converts the equation into the power Kadomtsev-Petviashvili equation [ut+unux+uxxx]x+uyy=0. Solitary wave solutions and cnoidal wave solutions are obtained. The cnoidal wave solutions are shown to be representable as infinite sums of solitons by using Fourier series expansions and Poisson's summation formula.http://dx.doi.org/10.1155/S0161171298000246Korteweg-de Vries equationKadomtsev-Petviashvili equation solitary wave solutioncnoidal wave solution. |
| spellingShingle | Yunkai Chen Nearly conconcentric Korteweg-de Vries equation and periodic traveling wave solution International Journal of Mathematics and Mathematical Sciences Korteweg-de Vries equation Kadomtsev-Petviashvili equation solitary wave solution cnoidal wave solution. |
| title | Nearly conconcentric Korteweg-de Vries equation and periodic traveling wave solution |
| title_full | Nearly conconcentric Korteweg-de Vries equation and periodic traveling wave solution |
| title_fullStr | Nearly conconcentric Korteweg-de Vries equation and periodic traveling wave solution |
| title_full_unstemmed | Nearly conconcentric Korteweg-de Vries equation and periodic traveling wave solution |
| title_short | Nearly conconcentric Korteweg-de Vries equation and periodic traveling wave solution |
| title_sort | nearly conconcentric korteweg de vries equation and periodic traveling wave solution |
| topic | Korteweg-de Vries equation Kadomtsev-Petviashvili equation solitary wave solution cnoidal wave solution. |
| url | http://dx.doi.org/10.1155/S0161171298000246 |
| work_keys_str_mv | AT yunkaichen nearlyconconcentrickortewegdevriesequationandperiodictravelingwavesolution |