Conservation laws, stability analysis, and dynamics of dispersive optical soliton solutions for higher-order nonlinear Schrödinger model with applications in single-mode optical fibers

The propagation of ultra-short light pulses in a monomode optical fiber is governed by a higher-order nonlinear Schrödinger equation, which constitutes its foundation. In this study, we constructed different optical solitons and wave solutions based on the modified generalized Riccati equation mapping approach for this dynamical model. The proposed approach finds applications in engineering, mathematics, physics, fiber optic communications, nonlinear optics, plasma physics, quantum optics and computing, biophysics, and condensed matter physics. To bridle the explanatory power, we analytically described the existence conditions pertaining to the above-mentioned soliton types by varying the relevant model parameters: bright and dark solitons, periodic solitons, singular solitons, peaked solitons, and peakon solitons. Then, solution profiles were graphically illustrated, portraying their dynamics and structural characteristics. The stability of the solutions was then cross-checked through modulation instability analysis as a crude means to check their accuracy and robustness. Thus, the model proposed above is effective.