Observations on the class of "Balancing Principle" for nonlinear PDEs that can be treated by the auxiliary equation method. (June 2015)

• Record Type: Journal Article
• Authors: Pınar, Zehra; Öziş, Turgut
• Is Part Of: Nonlinear analysis. Volume 23(2015)
• Page Start: 9
• Page End: 16
• Publication Date: 2015-06
• Subjects: Balancing principle -- Travelling wave solutions -- Nonlinear PDE; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2014.11.001
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: There is collection of methods for finding explicit travelling wave solutions of nonlinear partial differential equations (NLPDEs) in the literature. Quite a large amount of these methods employ "Balancing Principle" in their methodology and they work for positive integer values only. Yet there is no well established formula for balancing and there is no specific rule to determine adequate balancing principle that works for any number which is positive/or negative and/or rational. In this study, we propose a new balancing principle which works for large range of the numbers either positive/or negative and/or rational that makes it possible to obtain new and original explicit travelling wave solutions of nonlinear partial differential equations (NLPDEs).