Analytical soliton solutions and dynamic behaviors of a fractional nonlinear model in relativistic wave mechanics

This article studied the quadratic fractional Klein–Fock–Gordon (KFG) equation in (1 + 1)-dimensions and solved it using the ϕ6-model expansion method. The governing equation arises in various real-life phenomena, including relativity, quantum field theory, and condensed matter physics, among others. Expressing a relation with a variable enables the conversion of this model’s partial differential equation formula into an ordinary differential equation, with solutions expressed in terms of hyperbolic, Jacobi elliptic, and trigonometric functions. A planar dynamical background is used to qualitatively assess the model, including a detailed analysis of bifurcation, chaos, and stability behaviors with diverse chaos-identification tools. This paper also seeks to permit us to finalize that the tactic is cooperative, advantageous, suitable, and comforting for the behavior of different kinds of nonlinear models.