New types of nonlinear waves and bifurcation phenomena in Schamel-Korteweg-de Vries equation
type: Item
instance of: scholarly article
title: New types of nonlinear waves and bifurcation phenomena in Schamel-Korteweg-de Vries equation
zbMATH Open document ID: 1293.35032
DOI: 10.1155/2013/483492
author: Yun Wu
author: Zhengrong Liu
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: We study the nonlinear waves described by Schamel-Korteweg-de Vries equation \(u_t+(au^{1/2}+bu)u_x+\delta u_{xxx}=0\). Two new types of nonlinear waves called compacton-like waves and kink-like waves are displayed. Furthermore, two kinds of new bifurcation phenomena are revealed. The first phenomenon is that the kink waves can be bifurcated from five types of nonlinear waves which are the bell-shape solitary waves, the blow-up waves, the valley-shape solitary waves, the kink-like waves, and the compacton-like waves. The second phenomenon is that the periodic-blow-up wave can be bifurcated from the smooth periodic wave.
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35C07
zbMATH DE Number: 6306869
zbMATH Keywords: compacton-like waves
zbMATH Keywords: kink-like waves
zbMATH Keywords: bell-shape solitary waves
zbMATH Keywords: valley-shape solitary waves
zbMATH Keywords: periodic-blow-up wave
Wikidata QID: Q58916397
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/483492
OpenAlex ID: W2117011163
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description: scientific article; zbMATH DE number 6306869