Dark Optical Soliton Solutions Research Articles

Pure-cubic optical solitons to the Schrödinger equation with three forms of nonlinearities by Sardar subequation method

In this work, it is used three families of nonlinearities such as Kerr law, Power Law and Parabolic law over the High-order dispersive Nonlinear Schrödinger equation to inquire optical soliton solutions and diverse solutions by employing the Sardar Sub-equation method. Considering the constraint relation on some parameters of the NLSE, it is obtained bright and dark optical soliton solutions. However, under a certain condition on the method parameters, it is exposed singular soliton and trigonometric function solutions. More precisely, for ρ=a24b, a new form of the complex solutions are obtained. The obtained results are depicted in 2D and 3D to show out the peakon soliton in Figure 2 compared to Yıldırım et al. (2020); Zayed et al. (2020) and Rezazadeh et al. (2020). These results could probably give a new way for designing optical fibers devices to update the communication flux.

Bright and dark optical solitons for (3 + 1)-dimensional hyperbolic nonlinear Schrödinger equation using a variety of distinct schemes

The current study is dedicated to furnish a class of bright soliton and dark soliton solutions for the (3 + 1)-dimensional hyperbolic nonlinear Schrödinger equation. In this direction we operate with a variety of schemes to derive a class of bright and dark optical soliton solutions. Moreover, we derive another class of solutions of distinct structures, that include periodic, complex, and exponential solutions. This analysis provides new findings with a variety of optical features.

W-shaped profile and breather-like soliton of the fractional nonlinear Schrödinger equation describing the polarization mode in optical fibers

We use the fractional nonlinear Schrödinger equation (FNLSE) to describe the polarization mode in optical fiber with Self-Steepening, Self-Frequency Shift, and Cubic-quintic terms to analyze the effects of the fractional time parameter (FTP) on bright and dark solitons as well as breather-like solitons. We use the transformation hypothesis and auxiliary equations method to obtain three families of solutions such as combined bright soliton, dark solitons, and rational solitons. We have shown the effects of the fractional parameter (FP) on the W-shaped profile, bright and dark optical soliton solutions as well as the corresponding chirp component. It is observed that for small values of the FP, optical soliton shape is affected and the soliton is unstable. Moreover, one observes the effects of fraction time on Modulation Instability (MI) gain spectra and MI bands. For certain values of the FP, it is formed sides lobes and for specific small values of the FP, both stability zone increases and amplitude of the MI gain increase while the stability zones increase. To confirm the robustness of the analytical results, we have used a numerical investigation. One exhibits the formation of breathers-like soliton with stable amplitude for small values of the FTP. It results from this study that the FP is efficient and can be used as an energy source where soliton or breathers-like soliton are involved for communication in optical fibers.

A variety of bright and dark optical soliton solutions of an extended higher-order Sasa–Satsuma equation

In this work we examine an extended nonlinear (2+1)-dimensional Sasa–Satsuma equation that covers the effect of perturbations. The extended model includes fourth-order spatial derivatives. We study the influence of the nonlinearity and spatial dispersions effects given in spatial directions x and y. We formally derive a variety of optical soliton solutions, that include bright, dark, exponential, singular, and rational solutions. We employ useful techniques to retrieve this variety of optical soliton solutions.

The Modified Exp (-vartheta(sigma)) -Expansion Function Method For Exact Solutions Of The Simplified MCH Equation And The Getmanou Equation

The present research explores, the modified exp -expansion function method (MEFM) is tested by applying it to obtain the exact travelling wave solutions for the simplified MCH equation and the Getmanou equation. Dark optical soliton solutions and dark-bright optical soliton solutions of the simplified MCH equation and the Getmanou equation are successfully constructed by using this method. We carry out all the computations and draw the 2D and 3D graph in this paper by Wolfram Mathematica 9. Besides, the graphical representation obviously shows forcefulness of this method.

Higher-order Sasa–Satsuma equation: Bright and dark optical solitons

In this work we present a generalized nonlinear (3+1)-dimensional Sasa–Satsuma equation. This equation is influenced by nonlinearity and spatial dissipations effects in all spatial directions. We formally retrieve bright and dark optical soliton solutions for this higher dimensional Sasa–Satsuma model. In addition, other singular and exponential solutions of distinct structures are derived.

Bright and dark optical solitons for a new (3+1)-dimensional nonlinear Schrödinger equation

In this work we address a new (3+1)-dimensional nonlinear Schrödinger equation influenced by cubic nonlinearity and spatial dissipations effects. We formally retrieve bright and dark optical soliton solutions for this higher dimensional Schrödinger model. In addition, other singular and periodic solutions of distinct structures are derived.

Two (3+1)-dimensional Schrödinger equations with cubic–quintic–septic nonlinearities: Bright and dark optical solitons

This work introduces two new sixth-order (3+1)-dimensional nonlinear Schrödinger equations with higher-order dispersive terms influenced by cubic–quintic–septic (CQS) nonlinearities. We formally retrieve bright and dark optical soliton solutions for each higher dimensional model. In addition, we find certain constraints on the parameters to determine these optical bright and dark solutions. Other solutions of distinct structures, such as singular solutions, are also formally determined.

Bright and dark optical solitons for (3+1)-dimensional Schrödinger equation with cubic–quintic-septic nonlinearities

This work addresses the soliton propagation for a sixth-order (3+1)-dimensional nonlinear Schrödinger equation with fourth-order and sixth-order dispersive terms under the influence of cubic–quintic–septic nonlinearities. We formally retrieve bright and dark optical soliton solutions for this equation. In addition, we find certain constraints on the parameters to determine these optical solutions. We employ other ansatze to determine other singular and periodic solutions. The obtained results may be helpful in understanding the wave dynamics in a cubic–quintic–septic nonlinear material such as chalcogenide glass.

Higher dimensional nonlinear Schrödinger equations in anomalous dispersion and normal dispersive regimes: Bright and dark optical solitons

In this paper, we are concerned with a higher order nonlinear Schrödinger equations existing in the anomalous dispersion regimes and the normal dispersive regimes. Applying the variational iteration method (VIM) we present bright soliton solutions for the anomalous case and dark optical soliton solutions for the normal dispersive regime. We address the constraint conditions that arise from the parameters involved in the model. Other solitonic, singular, and exponential solutions are derived as well.

Optical bright and dark soliton solutions for coupled nonlinear Schrödinger (CNLS) equations by the variational iteration method

This paper studies optical bright and dark soliton solutions for coupled nonlinear Schrödinger (CNLS) equations in the anomalous and dispersive regimes. We operate the variational iteration method (VIM) to derive a set of diverse types of bright and dark optical soliton solutions. The VIM gives the solution in a rapidly convergent series without any need for physical restrictions or changing the nonlinearity issue. The presented analysis shows the pertinent features of the VIM method in handling nonlinear evolution equations.

The complex Ginzburg Landau equation in kerr and parabolic law media

This paper study the complex Ginzburg-Landau equation with two different forms of nonlinearity. The Jacobi elliptic ansatz method is used to obtain the optical soliton solutions of this equation in the kerr and parabolic law media. Bright and dark optical soliton solutions are acquired as well as Jacobi elliptic function solutions. The existence criteria of these solutions are also indicated.

Bright, dark and Gaussons optical solutions for fourth-order Schrödinger equations with cubic–quintic and logarithmic nonlinearities

This work addresses two nonlinear Schrödinger equations with fourth-order dispersion and cubic–quintic nonlinearity for the first one, and logarithmic nonlinearity for the second. The proposed methods retrieve bright and dark optical soliton solutions for the first equation, whereas Gausson soliton solutions will be obtained for the logarithmic Schrödinger equation. The obtained Gaussons are characterized by no soliton radiation, and propagate through dispersion-managed optical fibers. In addition, with some certain constraints on the parameters, other solutions are derived. The obtained results may be helpful in understanding the solitons features in optical fiber.

Optical soliton perturbation with Radhakrishnan–Kundu–Lakshmanan equation by Lie group analysis

This paper conducts Lie group analysis of the perturbed Radhakrishnan–Kundu–Lakshmanan equation to retrieve optical soliton solutions. This powerful integration scheme retrieves bright and dark optical soliton solutions to the model that is studied with power law nonlinearity. The existence criteria of such solitons are also presented.

Optical soliton perturbation with exotic non-Kerr law nonlinearities

This study secures singular and dark optical soliton solutions to the perturbed nonlinear Schrodinger’s equation that is studied with five different forms of nonlinearity. Two integration schemes are employed to retrieve these soliton solutions. They are csch method and the tanh method that successfully obtains the soliton solutions.

Optical solitons of transmission equation of ultra-short optical pulse in parabolic law media with the aid of Backlund transformation

The Backlund transformation is used to obtain optical soliton for a type of the Schrödinger equation. Kink-type and dark-optical soliton solutions are acquired of the Schrödinger equation. It is illustrated that the examined equation is integrable because if an equation has a Backlund transformation it could be integrable. Several constraint conditions for the parameters are derived that establish the existence of the soliton solutions. The numerical simulations supplement the analytical schemes.

Optical solitons of the coupled nonlinear Schrödinger’s equation with spatiotemporal dispersion

In this work, the coupled nonlinear Schrodinger’s equation (CNLSE) is studied with four forms of nonlinearity. The nonlinearities that are considered in this paper are the Kerr law, power law, parabolic law and dual-power law. Jacobi elliptic function solutions and also bright and dark optical soliton solutions are obtained for each law of the CNLSE. We will acquire constraint conditions for the existence of obtained solitons.

Optical Solitons with Power Law Nonlinearity and Hamiltonian Perturbations: An Exact Solution

This paper studies the optical solitons with power law nonlinearity in presence of Hamiltonian perturbation terms. The perturbation terms that are taken into account are inter-modal dispersion, third order dispersion, self-steepening term and nonlinear dispersion. An exact 1-soliton solution is obtained by the solitary wave ansatz. Both bright and dark optical soliton solutions are obtained. The domain restrictions have also been identified in the process.