Chaotic, bifurcation, sensitivity, modulation stability analysis, and optical soliton structure to the nonlinear coupled Konno–Oono system in magnetic field

In this research work, the nonlinear coupled Konno–Oono (CKO) system is under examination to explore the dynamical soliton wave structure in the magnetic field through two distinct approaches with qualitative analysis. The magnetic potential represents an essential tool in constructing diverse functions in the fluency of the magnetic field. Based on the nature and physical context of certain magnetic fields, the CKO nonlinear evolution system was raised to modify the magnetic effects. Such impacts on the dynamics for the CKO system depend on the magnetic potential. The current study aims to expand the use of the sine–cosine and tan–cotan methods to process the CKO equations analytically. The two techniques show the applicability, simplicity, and low complexity based on the traveling-wave procedure. Assorted bright, dark, and mixed closed-form soliton solutions have been derived. The 3D solitons with different structures have been depicted. The interaction of displacements inside the magnetic field is also shown. For more generality, and because of the new findings in real-life applications of fractional calculus, the time-fractional CKO model in different versions is discussed, and its effects are illustrated. Finally, we analyze the stability explorations for the corresponding nonlinear ordinary system out of its sensitivity, bifurcation, and chaotic behaviors.