Peaked and Smooth Solitons for K*(4,1) Equation
This paper is contributed to explore all possible single peak solutions for the K*(4,1) equation ut=uxu2+2α(uuxxx+2uxuxx). Our procedure shows that the K*(4,1) equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestal limξ→±∞u=A≠0 or possesses compa...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/518415 |
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| Summary: | This paper is contributed to explore all possible single peak solutions for the K*(4,1) equation ut=uxu2+2α(uuxxx+2uxuxx). Our procedure shows that the K*(4,1) equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestal limξ→±∞u=A≠0 or possesses compacton solutions only when limξ→±∞u=A=0. We present a new smooth soliton solution in an explicit form. Mathematical analysis and numeric graphs are provided for those soliton solutions of the K*(4,1) equation. |
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| ISSN: | 1110-757X 1687-0042 |