Observations on the class of “Balancing Principle” for nonlinear PDEs that can be treated by the auxiliary equation method

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).