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

Jianping Shi and Jibin Li

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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.

Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2014/893279

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:893279

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().