The periodic dark and bright solitons based on control fields of Milnor polynomial and super-Gaussian beam are investigated in a duplicated two-level atomic medium. The Milnor polynomial and super-Gaussian beam play an important role in the pulse, pulse intensity, and different types of solitons. The Milnor polynomial depends on the beam waist W, phase \(\Phi \) , and the super-Gaussian beam depends upon the variance of standard deviation \(\sigma \) , the power of super-Gaussian P, and the starting point \(z_0\) . The optical solitons are examined with the variation of detuning, decay rates, Rabi frequency of driving fields, and position ( \(z/\lambda \) ) and time ( \(t/\tau _0\) ) coordinates. The different types of solitons, such as periodic, dark, and bright solitons, are reported with Milnor-Gaussian and super-Gaussian beams as well as position and time coordinates. The shape of solitons is maintained by nonlinearity and dispersion. The soliton pulse intensity is studied as it varies with position and time, ranging from \(0.0025\%\) to \(100\%\) . The obtained results have significant applications in nonlinear optics, neural networks, hydrodynamics, traffic flow, soliton lasers, superconductivity, spectroscopy, amplifiers, and data transmission.
