## Abstract and Applied Analysis

### New Types of Nonlinear Waves and Bifurcation Phenomena in Schamel-Korteweg-de Vries Equation

#### Abstract

We study the nonlinear waves described by Schamel-Korteweg-de Vries equation ${u}_{t}+\left({au}^{1/2}+bu\right){u}_{x}+{\delta u}_{xxx}=0$. 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 483492, 18 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393512005

Digital Object Identifier
doi:10.1155/2013/483492

Mathematical Reviews number (MathSciNet)
MR3091224

Zentralblatt MATH identifier
1293.35032

#### Citation

Wu, Yun; Liu, Zhengrong. New Types of Nonlinear Waves and Bifurcation Phenomena in Schamel-Korteweg-de Vries Equation. Abstr. Appl. Anal. 2013 (2013), Article ID 483492, 18 pages. doi:10.1155/2013/483492. https://projecteuclid.org/euclid.aaa/1393512005

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