scholarly journals Optical solitons and modulation instability analysis to the quadratic-cubic nonlinear Schrödinger equation

2018 ◽  
Vol 24 (1) ◽  
pp. 20-33 ◽  
Author(s):  
Mustafa Inc ◽  
Aliyu Isa Aliyu ◽  
Abdullahi Yusuf ◽  
Dumitru Baleanu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Modulation Instability ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Integration Scheme ◽  
Instability Analysis ◽  
Nonlinear Schrödinger

This paper obtains the dark, bright, dark-bright, dark-singular optical and singular soliton solutions to the nonlinear Schrödinger equation with quadratic-cubic nonlinearity (QC-NLSE), which describes the propagation of solitons through optical fibers. The adopted integration scheme is the sine-Gordon expansion method (SGEM). Further more, the modulation instability analysis (MI) of the equation is studied based on the standard linear-stability analysis, and the MI gain spectrum is got. Physical interpretations of the acquired results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the PNSE.

scholarly journals Optical singular and dark solitons to the nonlinear Schrodinger equation in magneto-optic waveguides with anti-cubic nonlinearity.

2021 ◽  
Author(s):  
Thilagarajah Mathanaranjan ◽  
Hadi Rezazadeh ◽  
Mehmet Senol ◽  
Lanre Akinyemi
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Modified Simple Equation Method ◽  
Exact Soliton Solutions ◽  
Magneto Optic

Abstract The present paper aims to investigate the coupled nonlinear Schrodinger equation (NLSE) in magneto-optic waveguides having anti-cubic (AC) law nonlinearity. The solitons secured to magneto-optic waveguides with AC law nonlinearity are extremely useful to fiber-optic transmission technology. Three constructive techniques, namely, the (G'/G)-expansion method, the modified simple equation method (MSEM), and the extended tanh-function method are utilized to find the exact soliton solutions of this model. Consequently, dark, singular and combined dark-singular soliton solutions are obtained. The behaviours of soliton solutions are presented by 3D and 2D plots.

The M-fractional improved perturbed nonlinear Schrödinger equation: Optical solitons and modulation instability analysis

2021 ◽  
pp. 2150121
Author(s):  
Eied M. Khalil ◽  
T. A. Sulaiman ◽  
Abdullahi Yusuf ◽  
Mustafa Inc
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Modulation Instability ◽  
Nonlinear Schrodinger Equation ◽  
Instability Analysis ◽  
Nonlinear Schrödinger ◽  
The Stability ◽  
The Waves

In order to obtain some novel analytical solutions for fractional improved nonlinear Schrodinger equation with perturbation, the polynomial expansion, simplest equation and extended sine-Gordon expansion schemes are utilized. A collection of different types of solitons are reported with a physical and important perspective, containing optical dark solitons. The methods reveal the solutions in a structure of rapidly converging series. This research highlights additional important features of the methods being considered. In addition, the modulation instability analysis is carried out to discuss the stability analysis of the solutions reached, and the movement role of the waves is examined, which affirms that all the established solutions are exact and stable.

Study of modulation instability analysis and optical soliton solutions of higher-order dispersive nonlinear Schrödinger equation with dual-power law nonlinearity

2019 ◽  
Vol 33 (25) ◽  
pp. 1950309
Author(s):  
Naila Nasreen ◽  
Aly R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Power Law ◽  
Schrodinger Equation ◽  
Modulation Instability ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Mapping Technique ◽  
Nonlinear Schrödinger ◽  
Dual Power

In this paper, based on proposed Riccati mapping technique, we investigated the soliton solutions of fourth-order dispersive nonlinear Schrödinger equation with nonlinearity of dual-power law. The various types of solitons solutions involving some parameters are constructed. These soliton solutions can be useful for understanding the physical nature of the waves spread in the dispersive medium. Furthermore, the Modulation Instability (MI) is discussed by standard linear-stability analysis that shows all achieved results are exact and stable. The movements of some achieved results were presented graphically by giving suitable values to parameters that provide easy understanding to the physical phenomenon of this dynamical model. The obtained results show the simplicity and efficiency of the current used approach.

scholarly journals On the optical solutions to nonlinear Schrödinger equation with second-order spatiotemporal dispersion

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 111-118
Author(s):  
Hadi Rezazadeh ◽  
Waleed Adel ◽  
Mostafa Eslami ◽  
Kalim U. Tariq ◽  
Seyed Mehdi Mirhosseini-Alizamini ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Group Velocity Dispersion ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Second Order ◽  
Wave Transformation ◽  
Nonlinear Schrödinger

Abstract In this article, the sine-Gordon expansion method is employed to find some new traveling wave solutions to the nonlinear Schrödinger equation with the coefficients of both group velocity dispersion and second-order spatiotemporal dispersion. The nonlinear model is reduced to an ordinary differential equation by introducing an intelligible wave transformation. A set of new exact solutions are observed corresponding to various parameters. These novel soliton solutions are depicted in figures, revealing the new physical behavior of the acquired solutions. The method proves its ability to provide good new approximate solutions with some applications in science. Moreover, the associated solution of the presented method can be extended to solve more complex models.

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