Analytic bounded travelling wave solutions of some nonlinear equations II

Eugenia N. Petropoulou, Panayiotis D. Siafarikas and Ioannis D. Stabolas

Chaos, Solitons & Fractals, 2009, vol. 41, issue 2, 803-810

Abstract: Using a functional analytic method, it is proven that an initial value problem for a general class of higher order nonlinear differential equations has a unique bounded solution in the Banach space H1(Δ) of analytic functions, defined in the open unit interval Δ=(-1,1). This result is also used for the study of travelling wave solutions of specific nonlinear partial differential equations, such as the KdV equation, the compound KdV–Burgers equation, the Kawahara equation, the KdV–Burgers–Kuramoto–Sivashinsky equation and a 7th order generalized KdV equation. For each one of these equations, it is proven that there are analytic, bounded travelling wave solutions in the form of power series which are uniquely determined once the initial conditions are given. The method described in this paper verifies all the travelling wave solutions of these equations which have also appeared in recent papers.

Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077908001525
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:41:y:2009:i:2:p:803-810

DOI: 10.1016/j.chaos.2008.04.002

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. ().