Comparative Analysis of Exact Solutions for the Phi-four Equation

Year 2019, , 496 - 500, 15.07.2019

Şamil Akçağıl

https://doi.org/10.17714/gumusfenbil.509053

Abstract

The Phi-4 equation plays an important role in mathematical physics and
it is particular form of the Klein-Gordon equation that models the phenomenon
in particle physics. This significant equation has been studied by many
researchers and many solutions to this equation have been obtained by using
different methods. In this study, the solutions obtained by three important
methods have been focused on: The modified simple equation method, the ansatz
method 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 and differences
of the obtained solutions have been compared with each other. In addition to
its easy applicability, the sn-ns method was shown to be highly effective and
reliable method.

Keywords

Ansatz method, He's variational method, Modified simple equation method, Phi-four equation, Sn-ns method

Phi-four Denkleminin Tam Çözümlerinin Karşılaştırmalı Analizi

Abstract

Matematiksel fizikte önemli bir rol oynayan Phi-4
denklemi, bu olguyu parçacık fiziğinde modelleyen Klein-Gordon denkleminin özel
bir halidir. Bu önemli denklem birçok araştırmacı tarafından çalışılmış ve bu denklemin
birçok çözümü farklı yöntemler kullanılarak elde edilmiştir. Bu çalışmada, üç
önemli yöntemle elde edilen çözümlere odaklanıldı: Modifiye edilmiş basit
denklem yöntemi, ansatz yöntemi ve He'nin varyasyonel yöntemi.  Phi-dört denklemi yeniden göz önüne alınarak,
daha önce elde edilmiş çözümlerin yanında yeni trigonometrik, hiperbolik ve
eliptik fonksiyon çözümleri sn-ns yöntemi kullanılarak elde edildi. Elde edilen
çözümlerin benzerlikleri ve farklılıkları birbirleriyle karşılaştırıldı. Kolay
uygulanabilirliğinin yanında, sn-ns metodun oldukça etkin ve güvenilir bir
yöntem olduğu gösterildi.

Keywords

Ansatz metodu, He'nin varyasyonel metodu, Modifiye edilmiş basit denklem metodu, Phi-four denklemi, Sn-ns metodu

References

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