Salam Khan

This paper retrieves an optical 1–soliton solution to a model that is written as a concatenation of the Lakshmanan–Porsezian–Daniel model and Sasa–Satsuma equation. The method of undetermined coefficients obtains a full spectrum of 1–soliton solutions. The multiplier approach yields the conserved densities, which subsequently lead to the conserved quantities from the bright 1–soliton solution.

The paper derives stationary optical solitons with nonlinear chromatic dispersion. A nonlocal form of nonlinearity and quintuple power–law of nonlinearity are considered. The Kudryashov’s integration scheme enables to retrieve such solitons. A plethora of solitons come with this algorithm.

The current work is devoted to investigating the multidimensional solitons known as optical bullets in optical fiber media. The governing model is a (3+1)-dimensional nonlinear Schrödinger system (3D-NLSS). The study is based on deriving the traveling wave reduction from the 3D-NLSS that constructs an elliptic-like equation. The exact solutions of the latter equation are extracted with the aid of two analytic approaches, the projective Riccati equations and the Bernoulli differential equation. Upon applying both methods, a plethora of assorted solutions for the 3D-NLSS are created, which describe mixed optical solitons having the profiles of bright, dark, and singular solitons. Additionally, the employed techniques provide several kinds of periodic wave solutions. The physical structures of some of the derived solutions are depicted to interpret the nature of the medium characterized by the 3D-NLSS. In addition, the modulation instability of the discussed model is examined by making use of the linear stability analysis.

The current work addresses cubic–quartic solitons to compensate for the low count of the chromatic dispersion that is one of the major hindrances of soliton transmission through optical fibers. Thus, the present paper handles the cubic–quartic version of the perturbed Fokas–Lenells equation that governs soliton communications across trans-oceanic and trans-continental distances. The model is also considered with the power-law form of nonlinear refractive index that is a sequel to the previously reported result. This is a tremendous advancement to the previously known result that was only with the Kerr-law form of nonlinear refractive index. The present paper mainly contributes by generalizing the Kerr law of nonlinearity to the power law of nonlinearity. The prior results therefore fall back as a special case to the results of this paper. The semi-inverse variational principle yields a bright 1-soliton solution that is imperative for the telecommunication engineers to carry out experimental investigation before the rubber meets the road. Hamiltonian perturbation terms are included that come with maximum intensity. The soliton amplitude–width relation is retrievable from a polynomial equation with arbitrary degree. The parameter constraints are also identified for the soliton to exist.

This paper obtains highly dispersive optical solitons in fiber Bragg gratings with the Kerr law of a nonlinear refractive index. The generalized Kudryashov’s approach as well as its newer version makes this retrieval possible. A full spectrum of solitons is thus recovered.

This paper secures solitary waves and conservation laws to the familiar Korteweg–de Vries equation and Gardner’s equation with three dispersion sources. The traveling wave hypothesis leads to the emergence of such waves. The three sources of dispersion are spatial dispersion, spatio–temporal dispersion and the dual-emporal–spatial dispersion. The conservation laws are enumerated for these models, evolved from the multiplier approach. The conserved quantities are computed with the solitary wave solutions that were recovered.

This work analytically recovers the highly dispersive bright 1–soliton solution using for the perturbed complex Ginzburg–Landau equation, which is studied with three forms of nonlinear refractive index structures. They are Kerr law, parabolic law, and polynomial law. The perturbation terms appear with maximum allowable intensity, also known as full nonlinearity. The semi-inverse variational principle makes this retrieval possible. The amplitude–width relation is obtained by solving a cubic polynomial equation using Cardano’s approach. The parameter constraints for the existence of such solitons are also enumerated.