Revealing homoclinic breather waves, periodic lump waves and other waves forms of an integrable reduced spin Hirota-Maxwell-Bloch system

In this manuscript, we investigate various wave forms of an integrable reduced spin Hirota-Maxwell-Bloch system, which accounts for the femtosecond pulses transmitted in an erbium doped fibre. We achieved this using periodic wave and logarithmic transformations. We investigated homoclinic breather waves, periodic lump waves, mixed waves, M-shaped waves interacting with kink and rogue waves and multi waves. Using carefully selected parameter values based on physical relevance, mathematical constraints, and stability analysis, we present three-dimensional plots and their accompanying contour and density maps for the homoclinic breather and periodic lump wave solutions using Mathematica. The solutions and their physical structures obtained explain the soliton phenomena and mimic the dynamic features of the travelling wave distortion front formed in the dispersive medium. It also illustrates the periodic wave and logarithmic transformations technique's strength, applicability, and future research opportunities in finding special solutions for a variety of nonlinear equations in physical science and engineering. Finally, as far as we could verify, this is the first work in the literature in which these ansatz functions are derived for this integrable reduced spin Hirota-Maxwell-Bloch system using logarithmic transformations.