Bifurcation analysis and new waveforms to the fractional KFG equation

This study presents novel waveforms and bifurcation analysis for the fractional Klein-Fock-Gordon (KFG) structure, which is widely used in particle and condensed matter physics. To examine the bifurcation, chaos, and sensitivity of the model, we derive the dynamic system equation from the Galilean transformation. We present and explore a diverse range of waveforms, including periodic waves, quasi-periodic waves, bright and dark solitons, kink waves, and anti-kink waves. Graphic diagrams from simulations illustrate the diverse features and existence of these solutions. Nonlinear models can benefit from the potency, brevity, and effectiveness of integration procedures used in contemporary scientific and engineering contexts.