Exploring novel solitary wave phenomena in Klein–Gordon equation using $$\phi ^{6}$$ ϕ 6 model expansion method

Exploring novel solitary wave phenomena in Klein–Gordon equation using $$\phi ^{6}$$ ϕ 6 model expansion method

Abstract In this study, the $$\phi ^{6}$$ ϕ 6 -model expansion method is showed to be useful for finding solitary wave solutions to the Klein–Gordon (KG) equation. We develop a variety of solutions, including Jacobi elliptic functions, hyperbolic forms, and trigonometric forms, so greatly enhancing...

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Bibliographic Details
Main Authors: Yasir A. Madani, Khidir Shaib Mohamed, Sadia Yasin, Sehrish Ramzan, Khaled Aldwoah, Mohammed Hassan
Format: Article
Language:English
Published: Nature Portfolio 2025-01-01
Series:Scientific Reports
Subjects:
Jacobi elliptic function (JEF)
Nonlinear equations
Singular solutions
Periodic solutions
Online Access:https://doi.org/10.1038/s41598-025-85461-w
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https://doi.org/10.1038/s41598-025-85461-w

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