A note on class of traveling wave solutions of a non-linear third order system generated by Lie’s approach

Alfred Huber

Chaos, Solitons & Fractals, 2007, vol. 32, issue 4, 1357-1363

Abstract: In this paper, Lie’s method is used to calculate solutions of a third order non-linear system of partial differential equations (nPDE). In our previous paper [Huber A. Appl Math Comput 2005;166/2:464], we have applied the tanh-method to generate solutions, in this case special class of solutions in form of traveling wave results (single soliton solutions as well as class of irregular solutions). Therefore, general families of solutions are of basic interest. Moreover, a complete characterization of the group properties is given. We determine the Lie point symmetry vector fields and calculate similarity “ansätze” for the first time. Further, we also derive a few non-linear transformations and some similarity solutions are obtained. The main purpose for the application of Lie’s method is of course the fact that we are able to calculate class of general solutions which do not underlie such strong restrictions as in the case of traveling wave “ansätze”. Otherwise, it is necessary to perform a group analysis in order to improve the solution manifold by an alternative way. Moreover, a criterion for the integrability via the Painlevé-conjecture is given and further, families of solutions in term of elliptic functions are derived via Lie‘s approach for the first time. Although no extensive studies are known up to this time a physical background of the considered system cannot exclude in future.

Date: 2007
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077905011665
Full text for ScienceDirect subscribers only

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:eee:chsofr:v:32:y:2007:i:4:p:1357-1363

DOI: 10.1016/j.chaos.2005.11.078

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().