## Abstract and Applied Analysis

### Bifurcation Approach to Analysis of Travelling Waves in Nonlocal Hydrodynamic-Type Models

#### Abstract

The paper considers the nonlocal hydrodynamic-type systems which are two-dimensional travelling wave systems with a five-parameter group. We apply the method of dynamical systems to investigate the bifurcations of phase portraits depending on the parameters of systems and analyze the dynamical behavior of the travelling wave solutions. The existence of peakons, compactons, and periodic cusp wave solutions is discussed. When the parameter $n$ equals 2, namely, let the isochoric Gruneisen coefficient equal 1, some exact analytical solutions such as smooth bright solitary wave solution, smooth and nonsmooth dark solitary wave solution, and periodic wave solutions, as well as uncountably infinitely many breaking wave solutions, are obtained.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 893279, 12 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412606309

Digital Object Identifier
doi:10.1155/2014/893279

Mathematical Reviews number (MathSciNet)
MR3186985

Zentralblatt MATH identifier
07023254

#### Citation

Shi, Jianping; Li, Jibin. Bifurcation Approach to Analysis of Travelling Waves in Nonlocal Hydrodynamic-Type Models. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 893279, 12 pages. doi:10.1155/2014/893279. https://projecteuclid.org/euclid.aaa/1412606309

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