Comparative Analysis of Exact Solutions for the Phi-four Equation

Abstract

The Phi-4 equation plays an important role in mathematical physics and it is particular form of the Klein-Gordonequation that models the phenomenon in particle physics. This significant equation has been studied by manyresearchers and many solutions to this equation have been obtained by using different methods. In this study, thesolutions obtained by three important methods have been focused on: The modified simple equation method, the ansatzmethod and He's variational method. Reconsidering the phi-4 equation, the same solutions and new trigonometric,hyperbolic and elliptic function solutions have been obtained by using the sn-ns method. The similarities anddifferences of the obtained solutions have been compared with each other. In addition to its easy applicability, the sn-nsmethod was shown to be highly effective and reliable method.