Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation

Kenneth L. Jones, Xiaogui He and Yunkai Chen

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 24, 1-7

Abstract:

This paper is concerned with periodic traveling wave solutions of the forced generalized nearly concentric Korteweg-de Vries equation in the form of ( u η + u / ( 2 η ) + [ f ( u ) ] ξ + u ξ ξ ξ ) ξ + u θ θ / η 2 = h 0 . The authors first convert this equation into a forced generalized Kadomtsev-Petviashvili equation, ( u t + [ f ( u ) ] x + u x x x ) x + u y y = h 0 , and then to a nonlinear ordinary differential equation with periodic boundary conditions. An equivalent relationship between the ordinary differential equation and nonlinear integral equations with symmetric kernels is established by using the Green's function method. The integral representations generate compact operators in a Banach space of real-valued continuous functions. The Schauder's fixed point theorem is then used to prove the existence of nonconstant solutions to the integral equations. Therefore, the existence of periodic traveling wave solutions to the forced generalized KP equation, and hence the nearly concentric KdV equation, is proved.

Date: 2000
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/24/202387.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/24/202387.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:202387

DOI: 10.1155/S0161171200004336

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 ().