Peaked and smooth solitons for \(K^*(4,1)\) equation
type: Item
instance of: scholarly article
title: Peaked and smooth solitons for \(K^*(4,1)\) equation
zbMATH Open document ID: 1397.35265
DOI: 10.1155/2013/518415
author: Yongan Xie
author: Hualiang Fu
author: Shengqiang Tang
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: This paper is contributed to explore all possible single peak solutions for the \(K^*(4,1)\) equation \(u_t=u_xu^2+2\alpha(uu_{xxx}+2u_xu_{xx})\). Our procedure shows that the \(K^*(4,1)\) equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestal \(\lim_{\xi\to\pm\infty}u=A\neq0\) or possesses compacton solutions only when \(\lim_{\xi\to\pm\infty}u=A=0\). 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.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35C08
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 6950723
Wikidata QID: Q59002767
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/518415
OpenAlex ID: W2079865059
description: scientific article; zbMATH DE number 6950723