The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations

Yong Chen and Zhenya Yan

Chaos, Solitons & Fractals, 2006, vol. 29, issue 4, 948-964

Abstract: In this paper, based on the close relationship between the Weierstrass elliptic function ℘(ξ;g2,g3) and nonlinear ordinary differential equation, a Weierstrass elliptic function expansion method is developed in terms of the Weierstrass elliptic function instead of many Jacobi elliptic functions. The mechanism is constructive and can be carried out in computer with the aid of computer algebra (Maple). Many important nonlinear wave equations arising from nonlinear science are chosen to illustrate this technique such as the new integrable Davey–Stewartson-type equation, the (2+1)-dimensional modified KdV equation, the generalized Hirota equation in 2+1 dimensions, the Generalized KdV equation, the (2+1)-dimensional modified Novikov–Veselov equations, (2+1)-dimensional generalized system of modified KdV equation, the coupled Klein–Gordon equation, and the (2+1)-dimensional generalization of coupled nonlinear Schrodinger equation. As a consequence, some new doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Moreover solitary wave solutions and singular solitary wave solutions are also given as simple limits of doubly periodic solutions. These solutions may be useful to explain some physical phenomena. The algorithm is also applied to other many nonlinear wave equations. Moreover we also present the general form of the method.

Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S096007790500696X
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:29:y:2006:i:4:p:948-964

DOI: 10.1016/j.chaos.2005.08.071

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. ().