Search

This paper revisits the study of optical solitons that is governed by one of the three forms of derivative nonlinear Schrodinger’s equation that is also known as Chen–Lee–Liu model. This model is investigated by the aid of fully shifted Jacobi’s collocation method with two independent approaches. The first is discretization of the spatial variable, while the other is discretization of the temporal variable. It is concluded that the method of the current paper is far more efficient and reliable for the considered model. Numerical results illustrate the performance efficiency of the algorithm. The results also point out that the scheme can lead to spectral accuracy of the studied model.

This paper implements a multiplier approach to exhibit conservation laws in magneto-optic waveguides that maintain anti-cubic as well as generalized anti-cubic forms of the nonlinear refractive index. Three conservation laws are retrieved for each form of nonlinearity. They are power, linear momentum and Hamiltonian. The conserved quantities are computed from their respective densities.

GStudied in this work are embedded solitons with quadratic nonlinearity that includes the effect of spatio-temporal dispersion. Two integration schemes yield bright, dark, singular and combo singular soliton solutions from the continuous regime. The existence criteria for these solitons are also included.

This paper presents a numerical study of highly dispersive optical solitons that maintain a cubic–quintic–septic nonlinear (also know as polynomial) form of the refractive index. The Laplace–Adomian decomposition scheme is applied as a numerical algorithm to put the model into perspective. Both bright and dark soliton solutions are studied in this context. Both surface plots and contour plots of such solitons are presented. The error plots are also shown, demonstrating extremely low error measure values.

This paper recovers cubic–quartic optical solitons for Kudryashov’s law having dual form of generalized nonlocal nonlinearity. Hamiltonian type perturbation terms are included and these appear with maximum intensity. Bright, dark and singular solitons have emerged with the implementation of sine-Gordon equation method to the model.

This paper exhibits bright, dark, singular as well as combo optical highly dispersive solitons in birefringent fibers. The governing model is considered with four forms of nonlinear refractive index. The existence criteria for such solitons are also listed.

This paper secures exact bright, dark and singular soliton solutions with parabolic–nonlocal combo nonlinearity in polarization-preserving optical fibers. The included perturbation terms are all of Hamiltonian type. Subsequently, an analytical bright 1-soliton solution is recovered, in the presence of higher-order dispersion effects by semi-inverse variational principle.

This paper implements mathematically rigorous extended trial function algorithm to address cubic–quartic optical solitons in birefringent fibers having Kudryashov’s law of nonlinear refractive index. Three special cases of the power-law nonlinearity parameter are taken into consideration. Bright and singular optical solitons emerge from this analytical scheme.

This paper studies optical soliton perturbation that appears with Kerr law nonlinearity having spatio-temporal dispersion. The numerical scheme adopted is the variational iteration method. The perturbation terms are of Hamiltonian type and stem from inter-modal dispersion, self-steepening and nonlinear dispersion. Both bright and dark solitons are taken into consideration.

This work retrieves optical solitons having generalized anti-cubic nonlinearity in fiber Bragg gratings by implementing extended auxiliary equation method. The spectrum of solitons are enumerated along with their existence criteria.

This paper derives the conserved densities for the perturbed complex Ginzburg–Landau model which is addressed with a range of nonlinear forms. The densities are derived with the implementation of Lie symmetry analysis while the conserved quantities are obtained from the soliton solutions to the model. For two such nonlinear forms the Hamiltonian cease to exist since the corresponding integrals are rendered divergent.

The propagation of dark solitons through a optical fiber governed by the higher order nonlinear Schrodinger’s equation with cubic–quintic non-Kerr refractive index is examined. The extended rational sinh–cosh and/or extended rational sin–cos method investigates the existence of various forms of dark solitons such as chirped periodic, breathing and hole-like dark soliton structure in optical fibers.

In this paper, we apply the unified Riccati equation expansion method, as well as two forms of auxiliary equation methodology, to find highly dispersive optical solitons in the nonlinear Schrodinger’s equation having a polynomial law of the refractive index change. Bright, dark and singular solitons as well as periodic and Jacobi elliptic solutions are obtained that are presented together with their existence criteria.

Graphical abstract Cubic-quartic soliton transmission having power law of nonlinearity refractive index., Highlights • Optical soliton solutions for the perturbed nonlinear Schrodinger’s equation are revealed. • Quadratic-cubic nonlinearity is considered. • Bright optical solitons are retrieved by the help of the IADM. • The numerical results together with high level accuracy plots are exhibited. • The method proposed herein works with high degree of accuracy., This paper numerically retrieves cubic-quartic solitons having power law of nonlinearity refractive index. An improvement of the Adomian decomposition scheme is the adopted algorithm of this work. The results are displayed along with the established error analysis.

This paper implements F-expansion scheme to obtain Jacobi’s elliptic function to complex Ginzburg–Landau equation with two nonlinear forms. In the limiting case of the modulus of ellipticity, bright and dark soliton solutions emerge.

This paper obtains bright, dark and singular optical soliton solutions to the nonlinear Schrodinger's equation with anti-cubic nonlinearity. The Q − function method and extended direct algebraic method are applied. In addition to optical solitons, periodic singular solutions naturally emerge as a byproduct upon application of these integration algorithms. There are constraint conditions that guarantee the existence of soliton solutions.

This paper reveals optical soliton solutions for the perturbed nonlinear Schrodinger’s equation that is studied with quadratic–cubic nonlinearity. The mapping methods are utilized to retrieve these solitons which are of bright, dark and singular type.

Highly dispersive optical solitons are obtained for nonlinear Schrodinger's equation that is studied in absence of self-phase modulation. The effect of nonlinearity comes from perturbation terms. Jacobi's elliptic function expansion reveals bright and dark soliton solutions to the model.

We investigate the generation and stability of three-dimensional (3D) solitons in binary atomic Bose–Einstein condensates with spin–orbit coupling (SOC) and Super-Gaussian optical lattices. We examine the stability of 3D solitons using their norm and energy. The evolution of solitons is made more stable and their resistance to collapse more robust by the introduction of Gaussian lattices. Depending on the relative strength of SOC, the nonlinearity modulation parameter, and the lattice parameters, we observe stable solitons of the semi-vortex and mixed-mode type. In addition, we demonstrate the robustness of solitons in propagation and collisions.

This paper studies optical solitons in birefringent fibers with anti-cubic nonlinearity. The exp-function scheme retrieves singular and combo solitons. The existence criteria for these solitons are also presented.

We investigate a generalized nonlinear Schrodinger equation with higher-order effects such as pseudo-quintic nonlinearity and self-steepening effect. The model applies to the description of ultrashort pulse propagation in nonlinear materials exhibiting a negative index of refraction. Three new types of nonlinearly chirped W-shaped soliton solutions are derived for the first time by using the traveling-wave method. The obtained structures have new functional forms that are distinct from the usual W-shaped soliton solution reported within the context of optical fibers. An important characteristic of these envelope solitons is the nonlinear chirp that is directly proportional to the intensity of the pulse. It is shown that these chirped W-shaped structures are formed as a result of the exact balance among the group velocity dispersion, the self-steepening effect, and the pseudo-quintic nonlinearity. Exact chirped bright soliton solutions of the model were also obtained under appropriate conditions. Our results may raise the possibility of some experiments and potential applications related to left-handed materials in the presence of self-steepening nonlinearity.

In this paper, we investigate the (2+1)-dimensional coupled nonlinear Schrodinger equations with perturbed dispersion and nonlinearity, which govern the transverse effects in a nonlinear optical system. Using symbolic calculation, the vector one- and two-soliton solutions are obtained via the Hirota method. By choosing the perturbation $$\alpha (t)$$ of the dispersion rate of soliton transmission as different functions, we observe different dark and anti-dark soliton structures. Among other, the parabolic dark soliton, m-shaped and w-shaped anti-dark solitons, two kinds of s-shaped anti-dark solitons with different curvatures and an anti-dark soliton with a peak are displayed. Moreover, the effects of other free parameters on the phase shift and pulse width, and collision of solitons are discussed. These results are of potential significance for the study of ultrashort pulse lasers and optical logic switches.

This paper reveals bright, dark and singular solitons in fiber Bragg gratings with dispersive reflectivity having parabolic form of nonlinearity. The method of undetermined coefficients yielded such soliton solutions. The existence criteria of such solitons are also enumerated that are listed as constraint conditions.

Optical soliton solutions are recovered for fibers having anti-cubic nonlinear law. Bright, dark and singular optical soliton solutions are retrieved by the aid of three forms of integrability tools. The existence criteria for such solitons are also presented.

This paper obtains bright and singular optical solitons that are studied with anti-cubic nonlinearity in birefringent fibers. The extended trial function scheme gave way to these results. The existence criteria of such solitons are also indicated.

This paper secures bright optical solitons in presence of third and fourth order dispersion terms while group velocity dispersion term is absent. The perturbation terms that are included appear with full nonlinearity. The semi-inverse variational principle is implemented to secure such solutions.

In this work, symmetry reduction for nonlinear Schrodinger's equation with anti-cubic nonlinearity is determined by using the invariance of equations under Lie group of transformations. Using the similarity transformations the equation is reduced into system of ordinary differential equations. Corresponding to reduced ordinary differential equations, some exact solutions are obtained. These yields bright solitons, dark solitons, singular solitons and other explicit solutions. It is also pointed out that some of the results reported earlier are particular forms of current solutions.

This work is about highly dispersive optical solitons with Kerr and power law nonlinearity. Bright, dark and singular solitons are obtained from undetermined coefficients. This method proves that highly dispersive optical solitons are obtainable only with inter-modal and group velocity dispersions for both nonlinear forms.

This paper retrieves, bright, dark and singular highly dispersive optical solitons with quadratic-cubic law of nonlinearity. The F-expansion scheme is the integration algorithm adopted in the paper. There are other solutions to the model that are also recovered such as doubly periodic functions, Weierstrass elliptic functions and periodic solutions.

This paper applies extended trial function scheme to retrieve bright and singular optical soliton solutions to fiber Bragg gratings that maintains parabolic law nonlinearity. The existence criteria for the solitons are presented. Additional solutions, such as rational waves and periodic solutions, naturally emerge from the scheme as a byproduct.

This paper secures bright, dark, singular and various forms of highly dispersive combo optical soliton solutions when the nonlinear medium is of non-local type. The F-expansion mechanism is the integration tool. A wide range of additional solutions, including complexitons, are also listed that emerged from the scheme. The existence criteria of such solutions are also presented.

This paper successfully applied F-expansion algorithm to obtain highly dispersive optical solitons with cubic-quintic-septic nonlinearity. Bright, dark and singular solitons and their combinations thereof are listed. Their respective existence criteria are also indicated. Additional solutions such as periodic singular solutions as well as results in terms of Weierstrass elliptic function are also revealed from the scheme.

We study the formation of chirped kink similaritons in an optical transmitting non-Kerr medium under the influence of the Raman effect. The requirements concerning the optical material parameters for the existence of these propagating nonlinear waveforms are found. We show that such similariton structures are chirped linearly and that the chirping parameter allows us to control their dynamics efficiently. We also investigate the dynamical behaviors of these chirped self-similar pulses in both dispersion decreasing fiber and the periodic distributed amplification system.

A single bright highly dispersive optical soliton solution is recovered from semi-inverse variational principle. The model contains six power law nonlinear terms that constitute self-phase modulation effect which was proposed by Kudryashov. The amplitude–width relation of the soliton was finally recovered by Cardano’s approach with appropriate and necessary constraints that are presented.

We investigate numerically and analytically light propagation in a single spiral waveguide formed in a nonlinear dielectric medium, in the regime of low spatial frequency of the waveguide rotation. We present a general variational approach for computing soliton parameters analytically, which includes various types of nonlinearity. In the particular case of media with cubic-quintic nonlinearity, analytical expressions found are in very good agreement with the numerical findings.

This paper studies solitons in highly dispersive optical metamaterials with cubic–quintic nonlinearity in presence of detuning, inter-moda dispersion, self-steepening and nonlinear dispersion. Three forms of integration scheme retrieved solitons and other solutions to the model that included snoidal and snoidal waves. These algorithms retrieved bright, dark, singular as well as dark-singular combo solitons along with their respective existence criteria.

This paper obtains soliton solutions to perturbed Fokas-Lenells equation by the aid of exp-function approach. The perturbation terms are considered with full nonlinearity. Singular and combo-soliton solutions are presented along with their existence criteria.

This paper retrieves optical solitons in birefringent fibers having non-local nonlinearity in presence of four-wave mixing. Phase-matching conditions have been implemented to display these solitons. Bright, dark and singular soliton solutions are revealed. Department of Mathematics and Statistics at Tshwane University of Technology South African National Foundation --- 92052 IRF1202210126 National Research Foundation of Korea --- NPRP 8-028-1-001 Qatar National Research Fund (QNRF)

This paper secures optical soliton solutions with generalized anti-cubic nonlinearity by extended trial function scheme. Both chirped and chirp-free optical soliton solutions are recovered. Bright and singular soliton solutions are obtained from the scheme.

In this paper, to build soliton solutions of the governing equation, describing a propagation of sub-picosecond pulses with cubic-quintic nonlinearity and fourth-order dispersion in optical fibers, we use three methods: auxiliary equation, sine-cosine method and csch function method. The results obtained are 1-soliton solutions that propagate in the fiber optic and LHMs.

The multiplier approach has been adopted to derive the conservation laws for optical solitons with non-local form of nonlinearity. The four conserved quantities are obtained from the 1-soliton solution that has already been reported earlier. The results are in terms of Gauss’ hypergeometric functions whose convergence criteria are compatible with the soliton structure.

We investigate the existence and stability properties of nonlinearly chirped solitary waves on a continuous-wave background in nonlinear metamaterials with higher-order effects such as pseudo-quintic nonlinearity and self-steepening effect. Novel classes of chirped gray solitary pulses (dark pulses with nonzero minimum intensity) are derived by employing the traveling-wave method. The conditions for the formation of these localized pulses as well as the nonlinear chirp associated to them are presented. The stability of the obtained structures is also demonstrated numerically under finite initial perturbations. The results show that the envelope pulses obtained here represent new types of extremely robust nonlinear chirped structures in highly nonlinear metamaterials.

We investigate the Kaup-Newell equation that represents one of the forms of derivative nonlinear Schrodinger equation. The model applies to the description of sub-pico-second pulse propagation through an optical fiber. A special complex envelope traveling-wave method is applied to find a nonlinear equation with a fifth-degree nonlinear term describing the dynamics of field amplitude in the nonlinear media. It is shown that the phase associated to the obtained pulses has a nontrivial form and possesses two intensity dependent chirping terms in addition to the simplest linear contribution. A class of soliton solutions of the bright, dark and singular type are derived for the first time. The requirements concerning the optical material parameters for the existence of these chirped structures are also discussed.

This paper employs extended trial function scheme to derive soliton solutions in birefringent fibers with quadratic–cubic nonlinearity. The mathematical algorithm reveals bright and singular optical soliton solutions that are listed with their respective existence criteria.

This paper addresses optical solitons in birefringent fibers that is modeled by complex Ginzburg–Landau equation with Kerr law nonlinearity. Three forms of integration architecture retrieves soliton and other solutions to the model. The solitons are classified and their existence criteria are also presented.

We investigate the formation and propagation of multipole solitons (MSs) in a cold atomic gas with a parity-time (PT) symmetric potential. A $$\wedge $$-type three-level configuration is considered in the electromagnetically induced transparency arrangement. The PT potential is introduced through an effective magnetic field. Various types of MS solutions are studied theoretically, and the stability analysis of the solutions is discussed numerically, using the modified square-operator method. It is shown that the characteristics of MSs can be easily controlled and manipulated via adjusting the nonlinearity and the external magnetic field parameters.

We demonstrate three-dimensional (3D) vortex solitary waves in the (3+1)D nonlinear Gross–Pitaevskii equation (GPE) with spatially modulated nonlinearity and a trapping potential. The analysis is carried out in spherical coordinates, providing for novel localized solutions, and the 3D vortex solitary waves are built that depend on three quantum numbers. Our analytical findings are corroborated by a direct numerical integration of the original equations. It is demonstrated that the vortex solitons found are stable for the quantum numbers n ≤ 2 , l ≤ 2 and m = 0 , 1 , independent of the propagation distance.

In this study, soliton solutions with differential group delay, having parabolic law nonlinearity, are constructed. The exp(−ϕ(ξ))-expansion method has been utilized. Additional solutions, including plane wave solutions and periodic singular waves naturally emerge from the integration scheme.