Solitary Wave Solution of Kink and Anti-kink types for the KG Model

This paper seeks to derive solitary wave solutions for the nonlinear Klein- Gordon equation, using the tanh-coth method. These solutions are crucial to field theory, relativistic quantum mechanics, condensed matter physics, and elementary particles. The proposed approach is simple to use and produces generalized solitonic wave properties. This work helps to a better understanding of kink and anti-kink solo behavior in applied research. 2D and 3D graphs are presented to demonstrate the behavior of the found solutions for suitable free parameter values. Finally, the suggested technique may be expanded to include a variety of equations that are developing in new physics and applied science.