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In this article, we investigate the traveling wave solutions to the KleinGordon equation in (2+1)-dimension with special types of nonlinearity. The types include quadratic, cubic and polynomial nonlinearity. The Klein-Gordon equation assumes significant role in numerous types of scientific investigation such as in quantum field theory, nonlinear optics, nuclear physics, magnetic field etc. To investigate the aimed traveling wave solutions, we execute the (G /G)-expansion method. The attained solutions are in the form of hyperbolic, trigonometric and rational functions. The results acknowledged that the applied method is very efficient and suitable for discovering differential equations with various types of nonlinearity considered in optics and quantum field theory. The solutions of the Klein-Gordon equation with quadratic, cubic, and polynomials nonlinearity play a significant role in many scientific measures notably optics and quantum field theory.

Exact wave solutions to the (2+1)-dimensional Klein-Gordon equation with special types of nonlinearity