On the Korteweg-de Vries equation: an associated equation

Eugene P. Schlereth and Ervin Y. Rodin

International Journal of Mathematics and Mathematical Sciences, 1984, vol. 7, 1-15

Abstract:

The purpose of this paper is to describe a relationship between the Korteweg-de Vries (KdV) equation u t − 6 u u x + u x x x = 0 and another nonlinear partial differential equation of the form z t + z x x x − 3 z x z x x z = H ( t ) z . The second equation will be called the Associated Equation (AE) and the connection between the two will be explained. By considering AE, explicit solutions to KdV will be obtained. These solutions include the solitary wave and the cnoidal wave solutions. In addition, similarity solutions in terms of Airy functions and Painlevé transcendents are found. The approach here is different from the Inverse Scattering Transform and the results are not in the form of solutions to specific initial value problems, but rather in terms of solutions containing arbitrary constants.

Date: 1984
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/7/237357.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/7/237357.xml (text/xml)

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:hin:jijmms:237357

DOI: 10.1155/S0161171284000272

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().