This paper recovers quiescent optical solitons that are self-sustaining, localized wave packets that maintain their shape and amplitude over long distances due to a balance between nonlinearity and dispersion. When a soliton is in a state of quiescence, it means that it is stationary in both space and time. Quiescent optical solitons are typically observed in optical fibers, where nonlinearity and dispersion can lead to the formation of solitons. The concatenation model is considered to understand the behavior of optical pulses propagating through nonlinear media. Here, we consider the familiar nonlinear Schrödinger equation, the Lakshmanan–Porsezian–Daniel equation, and the Sasa–Satsuma equation. The current paper also addresses the model with nonlinear chromatic dispersion, a phenomenon that occurs in optical fibers and other dispersive media, where the chromatic dispersion of the material is modified by nonlinear effects. In the presence of nonlinearities, such as self-phase modulation and cross-phase modulation, the chromatic dispersion coefficient becomes a function of the optical intensity, resulting in nonlinear chromatic dispersion. A full spectrum of stationary optical solitons, along with straddled stationary solitons, are obtained. There are four integration schemes that made this retrieval possible. The numerical simulations are also included for these solitons. The parameter constraints also indicate the existence criteria for these quiescent solitons.

In the current study, the concatenation model of birefringent fibers is explored for the first time, and we present optical soliton solutions to the model. The integration algorithm used to achieve this retrieval is the method of undetermined coefficients, which yields a wide range of soliton solutions. The parameter constraints arise naturally during the derivation of the soliton solutions, which are essential for such solitons to exist.

The current paper implements three elegant approaches to recover a complete spectrum of optical solitons to the Radhakrishnan-Kundu-Lakshmanan equation with dual-power law of nonlinear refractive index. The conservation laws are also recovered by the usage of multipliers approach. The parameter constraints for the existence of such solitons are also enumerated. The numerical simulations of the recovered soliton solutions are also presented.

The paper concentrates on the solitary waves that are retrievable from the generalized Boussinesq equation. The numerical simulations are displayed in the paper that gives a visual perspective to the model studied in neurosciences. The Laplace–Adomian decomposition scheme makes this visualization of the solitons possible. The numerical simulations are being reported for the first time using an elegant approach. The results would be helpful for neuroscientists and clinical studies in Medicine. The novelty lies in the modeling that is successfully conducted with an impressively small error measure. In the past, the model was integrated analytically only to recover soliton solutions and its conserved quantities.

The paper addresses optical solitons in magneto-optic waveguides that are studied using Kudryashov’s law of nonlinear refractive index in the presence of chromatic dispersion and Hamiltonian-type perturbation terms. The trial solution approach yielded a variety of soliton solutions, which are listed in this paper.