The analytical study of soliton dynamics in fractional coupled Higgs system using the generalized Khater method

This study introduces the generalized Khater Method (gKM) as a tool for investigating the existence and dynamics of soliton solutions within the realm of the Fractional Coupled Higgs System (FCHS) with conformable fractional derivatives. The methodology involves obtaining Nonlinear Ordinary Differential Equations (NODEs) from FCHS via a fractional complex transformation. The reduced NODEs are further used to uncover various families of soliton solutions, elucidating their intricate interrelationships and dynamics. Using some 3D graphics, we visually depict the behavior of some soliton solutions, including shock, lump-type shock, periodic, multiple periodic, rogue, and kink solitons. These findings contribute to a better understanding of the dynamics inherent in the FCHS and have potential applications in domains dealing with nonlinear fractional partial differential equations. Arguably, the study also highlights the importance of incorporating the conformable fractional derivative into the FCHS to provide it with more degrees of freedom, which allows for a deeper exploration of its behaviors and could have significant implications for particle physics, particularly for phenomena such as mass origin and electroweak violation of symmetry.