Peaked and Smooth Solitons for K*(4,1) Equation

Yongan Xie, Hualiang Fu and Shengqiang Tang

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
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https://doi.org/10.1155/2013/518415

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:518415

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