Exploration of Soliton Solutions in Nonlinear Optics for the Third Order Klein-Fock-Gordon Equation and Nonlinear Maccari’s System

In this article, the main objective is to analytical investigation of the third order Klein-Fock-Gordon eation and the nonlinear Maccari’s system. The Klein-Fock-Gordon equation have vital applications in quantum field theory, article physics, condensed matter physics, astrophysics and cosmology. On the other hand, the nonlinear Maccari’s system significantly explain the neural dynamics, cardiac rhythms, population dynamics and case study for theoretical analysis and the development of mathematical techniques. In order to develop the analytical exact soliton solutions for these considered nonlinear models, the modified Kudryashov’s and extended Kudryashov’s methods are utilized and numerous kinds of soliton wave structures constructed such as dark soliton, bright soliton, dark-bright soliton and exponential solutions which are not discussed before this study along with utilized analytical techniques. The obtained soliton solutions describe the propagation of spin-0 particles like mesons behave according to a relativistic wave equation in quantum field theory. The constructed soliton wave structures of the Klein-Gordon equation represent localized, stable, and particle-like excitations of the scalar field described by the equation and can be interpreted as "quasi-particles" or "wave packets" which propagate through the field while maintaining their shape and energy. The nonlinear Maccari’s system’s soliton profiles offer potential solutions for issues like information processing, signal transmission, and pulse shaping. They also provide a framework for comprehending and modifying wave-like phenomena in complex systems. The graphical demonstration of their propagation in three-dimensional, contour and two dimensional is presented with suitable parametric values.