Peaked and smooth solitons for [K.sup.] equation

This paper is contributed to explore all possible single peak solutions for the [K.sup.*] (4,1) equation [u.sub.t] = [u.sub.x][u.sub.2] + 2a([uu.sub.xxx] + 2[u.sub.x][u.sub.xx]). Our procedure shows that the [K.sup.*](4,1) equation either has peakon, cuspon, and smooth soliton solutions when sitting...

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Bibliographic Details
Published in:Journal of applied mathematics 2013-01
Main Authors: Xie, Yongan, Fu, Hualiang, Tang, Shengqiang
Format: Article
Language:English
Subjects:
Differential equations, Nonlinear
Differential equations, Partial
Mathematical research
Smoothing (Statistics)
Solitons
Online Access:Get full text
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Summary:This paper is contributed to explore all possible single peak solutions for the [K.sup.*] (4,1) equation [u.sub.t] = [u.sub.x][u.sub.2] + 2a([uu.sub.xxx] + 2[u.sub.x][u.sub.xx]). Our procedure shows that the [K.sup.*](4,1) equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestal [lim.sub.ξ[right arrow]±∞] u = A ≠ 0 or possesses compacton solutions only when [lim.sub.ξ→±∞] u = A = 0. We present anew smooth soliton solution in an explicit form. Mathematical analysis and numeric graphs are provided for those soliton solutions of the [K.sup.*](4,1) equation.
ISSN:1110-757X
DOI:10.1155/2013/518415