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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171298000246 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |