Dynamical analysis of multi-soliton and interaction of solitons solutions of nonlinear model arise in energy particles of physics

Abstract

This study explores multi-soliton solutions and their interactions within the framework of the Klein-Fock-Gordon (K-F-G) equation. The K-F-G equation plays a crucial role in modeling relativistic wave phenomena and has diverse applications in describing energy particles in physics. The newly modified simple equation (NMSE) method is employed to analyze multi-soliton solutions and their interactions. Under specific conditions, novel families of solutions are derived and expressed through exponential and hyperbolic functions, as well as their combinations. The NMSE method is particularly effective in generating and analyzing a variety of soliton interactions, including multi-kink and anti-kink solutions, multi-bell-shaped solutions for bright-dark and dark-bright solitons, and combinations of kink, bell-shaped, and periodic solutions. These interactions are further illustrated through 3D visualizations, density plots, and contour maps. The simulation results demonstrate that the NMSE method works efficiently, is simple to use, and has versatility for a wide range of nonlinear evolution equations in computational physics and other interdisciplinary domains