Analytical treatment with the Nucci reduction technique on the p-forced nonlinear Klein-Gordon equation

Abstract

The main purpose of this study is to reach the exact solutions of the p-forced nonlinear Klein-Gordon equation by using a novel method called the Nucci reduction method. The nonlinear Klein-Gordon equation finds applications in various real-world scenarios. One notable application is in the field of nonlinear optics, where the equation is used to study the propagation of intense laser beams through nonlinear media. Nonlinear Klein-Gordon equations are also employed in condensed matter physics to model the behavior of superconductors and superfluids. Additionally, these equations have been used in cosmology to study the dynamics of scalar fields during the early universe and their role in inflationary models. The nonlinear Klein-Gordon equation has proven to be a valuable tool in understanding and predicting the behavior of scalar fields in a wide range of physical systems. Some exact solutions with the first integrals of the proposed model have been successfully achieved utilizing the Nucci reduction technique. In order to observe the strengths of the method, three-dimensional and density graphs of the solutions are presented.