A note on the Sine-Gordon expansion method and its applications
Nizhum Rahman
TL;DR
This paper applies the sine-Gordon expansion method to solve complex equations, deriving new soliton solutions in various functional forms and visualizing them with graphical software.
Contribution
It introduces the application of the sine-Gordon expansion method to new high-dimensional equations, producing novel soliton solutions in hyperbolic, complex, and trigonometric forms.
Findings
New soliton solutions in hyperbolic, complex, and trigonometric forms
Graphical visualization of solutions in 2D and 3D
Extension of the sine-Gordon expansion method to higher-dimensional equations
Abstract
The sine-Gordon expansion method; which is a transformation of the sine-Gordon equation has been applied to the potential-YTSF equation of dimension (3+1) and the reaction-diffusion equation. We obtain new solitons of this equation in the form hyperbolic, complex and trigonometric function by using this method. We plot 2D and 3D graphics of these solutions using symbolic software.
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Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations · Nonlinear Photonic Systems