Soliton propagation and evolution in 1D quantum systems: a study of higher-order dispersion and nonlinear effects

Nonlinear wave dynamics play an essential role in understanding energy localization, pulse transmission, and stability events in a variety of physical systems. Inspired by its importance, we study a fourth-order nonlinear Schrödinger equation in (1 + 1) dimensions with dispersion effects and higher-order nonlinear interactions. The intricate behavior of nonlinear optical pulses and other physical systems displaying high-order effects is well captured by this model. Three potent analytical techniques are the Sardar sub-equation method; sine-Gordon expansion method; G′/(bG′ + G + a)-expansion method to generate a variety of accurate solutions in order to obtain analytical insights. Under certain parametric conditions, these methods extract periodic, dark, singular, dark-bright, dark-singular, and singular-periodic soliton-type solutions. A better grasp of nonlinear wave modulation and evolution is provided by the associated graphical representations, which clarify how changes in parameters affect the wave profiles. Additionally, the modulation instability analysis verifies the stability and physical consistency of the generated soliton solutions. The design and control of ultra-short pulse propagation in nonlinear optical fibers and photonic communication systems can benefit from the study’s conclusions.