Fractals and Chaotic Solitons Phenomena in Conformable Coupled Higgs System

The current study aims to construct and examine a new plethora of soliton solutions for the conformable coupled Higgs system (CCHS), a system of nonlinear fractional partial differential equations (NFPDEs) which was initially presented utilize a systematic structure to consider the responsive mechanism of the Higgs system in the electroweak theory perspective, within the framework of the standard model of physics. To achieve our goal, we utilize a transformation-based analytical technique, namely, the generalized Bernoulli equation method (gBEM), which reduces CCHS to nonlinear ordinary differential equations (NODEs) via a fractional complex transformation. The fresh assortment of soliton solutions is produced when the resultant NODEs are tackled using the Maple tool. We employ 3D and contour visualizations to graphically represent the behavior of acquired solitons, which prominently reveal that these soliton solutions show axial, chaotic, and periodic perturbations which induce instabilities in soliton and may lead to the formation of fractals. The results appear groundbreaking, showcasing diverse families of soliton solutions with intricate interrelations and dynamics. These findings not only advance our theoretical understanding of CCHS dynamics but they may also have implications in NFPDE–related fields.