The compatibility and dynamics of optical soliton solutions for higher-order nonlinear Schrödinger model

The nonlinear Schrödinger equation describes a wide spectrum of non-linear wave phenomena across different fields of physics and engineering, including optical pulse transmission, propagation of intense light pulses, soliton propagation, quantum optics, self-phase modulation, dynamics of ultra-cold atomic gases, non-linear dynamics of plasma waves, dynamics of wave packets, quantum information theory, etc. In this study, we investigate the higher-order non-linear Schrödinger equation (hNLSE) and the perturbed non-linear Schrödinger equation (pNLSE) with Kerr law non-linearity by using a conformable and reliable expansion scheme. The solutions are constructed in terms of transcendental functions, specifically the exponential and trigonometric functions, and their dynamics are explained through two-, three-dimensional, and contour plots using the symbolic computation software Mathematica for certain parameter values, exhibiting soliton characteristics within the defined ranges. The solutions exhibit distinct soliton characteristics, like kink-shaped, one-sided kink-shaped, anti-bell-shaped, parabolic-shaped, and others. The solutions attained are compared with those documented in the existing literature, which highlights their originality. The obtained soliton solutions hold potential for theoretical analysis of soliton propagation, non-linear dynamics of plasma waves and ultra-cold atomic gases, communications through optical fiber, etc.