Search

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 and lists optical solitons of perturbed Kudryashov’s model with arbitrary refractive index. Dark, singular and combo singular soliton solutions are identified with five integration schemes. These are visible along with their respective existence criteria.

This paper obtains optical soliton solutions of the Kudryashov’s model with arbitrary refractive index. Three integration algorithms collectively revealed a full spectrum of single solitons along with a straddled soliton. The constraint conditions for the existence of such solitons are also listed. Finally, the only conserved quantity, supported by the model, is penned down.

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 recovers cubic–quartic optical solitons for perturbed Lakshmanan–Porsezian–Daniel model. This is for both with and without polarization. The sine-Gordon equation approach is the scheme adopted to retrieve the soliton solutions. A full spectrum of soliton solutions have emerged.

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.

In this paper, the extended Kudryashov’s method has been successfully implemented to obtain optical solitons and other solutions to Kudryashov’s model in fiber Bragg gratings. Dark and singular optical solitons emerge from the scheme along with their respective existence criteria.

This paper recovers optical solitons for the newly proposed Kudryashov’s equation which governs soliton pulse propagation through optical fibers and photonic crystal fibers. A spectrum of soliton solutions are obtained from a wide range of integration norms. The existence criteria for such solitons are enlisted. Finally, couple of numerical simulations make the paper rounded.

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 paper addresses optical solitons in birefringent fibers modeled by Radhakrishnan–Kundu–Lakshmanan equation in coupled vector form. Bright, dark and singular solitons are recovered by trial and modified simple function principles.

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 reports conservation laws for highly dispersive optical solitons in birefringent fibers. Three forms of nonlinearities are studied which are Kerr, polynomial and nonlocal laws. Power, linear momentum and Hamiltonian are conserved for these types of nonlinear refractive index.

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.

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.

This paper studies polarized cubic–quartic solitons that are modeled by Fokas–Lenells equation in birefringent fibers. Two integration schemes recovered a spectrum of soliton solutions to the model. Subsequently, the bright solitons compute the corresponding conserved quantities from the respective densities that are recovered by the multiplier approach.

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.

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 soliton solutions to Kaup–Newell's equation in optical fibers. Two fundamental integration schemes, namely the csch-function method and traveling wave hypothesis, obtain singular and bright soliton solutions respectively. The existence criteria for these solitons are also presented.

This paper retrieves bright, dark and singular solitons of both types for Bragg gratings with dispersive reflectivity. The method of undetermined coefficients is the integration algorithm adopted in this paper. Several constraints guarantee the existence of such solitons.

Optical soliton solutions are retrieved for Lakshmanan–Porsezian–Daniel equation by employing Riccati equation approach. The soiton solutions that are presented are generalized versions of solutions that have been reported in the past. The constraint conditions guarantee the existence of such solitons.

This paper retrieves optical solitons in fiber Bragg gratings, with dispersive reflectivity, by extended trial function approach. Bright and singular soliton solutions are listed and the corresponding integrability conditions are also enumerated.

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 investigate the propagation of self-similar optical solitons on a continuous-wave background through a non-centrosymmetric waveguide with second- and third-order nonlinearities. The generalized inhomogeneous nonlinear Schrodinger equation with quadratic–cubic nonlinearities and gain or loss is used to describe the beam propagation through the waveguide. Three new types of exact self-similar localized solutions propagating on a continuous-wave background are found under certain parametric conditions. The self-similar wave solutions comprise bright solitons, W-shaped, and kink solitons. The dynamic behaviors of these solitons are analyzed for a periodically distributed dispersion system.

The extended Jacobi's elliptic function scheme is implemented to retrieve bright, dark and singular highly dispersive optical solitons that is studied in cubic–quintic–septic nonlinear medium. These solitons evolve from Jacobi's elliptic functions when limiting value of the modulus of ellipticity approaches unity.

This paper conducts numerical studies of optical solitons with Lakshmanan–Porsezian–Daniel model having spatio-temporal dispersion. A newly proposed version of the well-known Adomian's decomposition method is applied to secure numerical simulations of the recently reported analytical soliton solutions. The focus of this paper stays with bright soliton solutions to the model.

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 employs two strategic integration algorithms to extract soliton solutions to Kundu-Eckhaus equation in the context of birefringent fibers. The two schemes are G′/G2-expansion approach and sine-cosine method. Bright, singular and dark-singular combo solitons are retrieved. With reversed constraint conditions, singular-periodic solutions also emerge, although they are not applicable to the photonics field.

This paper retrieves dark and singular solitons in birefringent fibers for quadratic-cubic nonlinear optical fibers. These solitons are presented with their respective integrability 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.

This work studies fractional temporal evolution of oblique resonant optical solitons in (3+1)-dimensions with Kerr- and parabolic-law nonlinearities. The generalized exp(−Φ(ξ))-expansion method along with the Khalil's conformable fractional derivatives is implemented to locate several forms of oblique resonant solitons. It is observed that obliqueness significantly modified resonant wave dynamics. The obtained results are very useful for understanding the dynamics of obliquely propagating resonant optical solitons and optical bullets.

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.

This paper retrieves chirped singular and bright-singular combo optical soliton solutions to the Chen–Lee–Liu equation. Three forms of independent intregration schemes are implemented to the model. They are csch function scheme, tanh–coth method and finally the modified simple equation approach. The integrability criteria for these are also presented.

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.