On the conformable nonlinear Schrödinger equation with second order spatiotemporal and group velocity dispersion coefficients

2021 ◽  
Author(s):  
Hadi Rezazadeh ◽  
Meryem Odabasi ◽  
Kalim U. Tariq ◽  
Reza Abazari ◽  
Haci Mehmet Baskonus
Keyword(s):  
Schrödinger Equation ◽  
Group Velocity ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Velocity Dispersion ◽  
Group Velocity Dispersion ◽  
Nonlinear Schrodinger Equation ◽  
Second Order ◽  
Dispersion Coefficients ◽  
Nonlinear Schrödinger

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.

scholarly journals Regular perturbation on the group-velocity dispersion parameter for nonlinear fibre-optical communications

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Vinícius Oliari ◽  
Erik Agrell ◽  
Alex Alvarado
Keyword(s):  
Schrödinger Equation ◽  
Group Velocity ◽  
Optical Fibre ◽  
Schrodinger Equation ◽  
Velocity Dispersion ◽  
Group Velocity Dispersion ◽  
Nonlinear Schrodinger Equation ◽  
Dispersion Parameter ◽  
Regular Perturbation ◽  
Fibre Channel

AbstractCommunication using the optical fibre channel can be challenging due to nonlinear effects that arise in the optical propagation. These effects represent physical processes that originate from light propagation in optical fibres. To obtain fundamental understandings of these processes, mathematical models are typically used. These models are based on approximations of the nonlinear Schrödinger equation, the differential equation that governs the propagation in an optical fibre. All available models in the literature are restricted to certain regimes of operation. Here, we present an approximate model for the nonlinear optical fibre channel in the weak-dispersion regime, in a noiseless scenario. The approximation is obtained by applying regular perturbation theory on the group-velocity dispersion parameter of the nonlinear Schrödinger equation. The proposed model is compared with three other models using the normalized square deviation metric and shown to be significantly more accurate for links with high nonlinearities and weak dispersion.

Numerical Methods for the Derivative Nonlinear Schrödinger Equation

2018 ◽  
Vol 19 (3-4) ◽  
pp. 239-249 ◽  
Author(s):  
Shu-Cun Li ◽  
Xiang-Gui Li ◽  
Fang-Yuan Shi
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Second Order ◽  
Compact Scheme ◽  
Order Accuracy ◽  
Nonlinear Schrödinger ◽  
Accuracy Order ◽  
Derivative Nonlinear Schrödinger Equation

AbstractIn this work, a second-order accuracy in both space and time Crank–Nicolson (C-N)-type scheme, a fourth-order accuracy in space and second-order accuracy in time compact scheme and a sixth-order accuracy in space and second-order accuracy in time compact scheme are proposed for the derivative nonlinear Schrödinger equation. The C-N-type scheme is tested to satisfy the conservation of discrete mass. For the two compact schemes, the iterative algorithm and the Thomas algorithm in block matrix form are adopted to enhance the computational efficiency. Numerical experiment is given to test the mass conservation for the C-N-type scheme as well as the accuracy order of the three schemes. In addition, the numerical simulation of binary collision and the influence on the solitary solution by adding a small random perturbation to the initial condition are also discussed.

Super and subluminal propagation in nonlinear Schrödinger equation model with self-steepening and self-frequency shift

2015 ◽  
Vol 24 (03) ◽  
pp. 1550033 ◽  
Author(s):  
A. Saini ◽  
V. M. Vyas ◽  
Thokala Soloman Raju ◽  
S. N. Pandey ◽  
Prasanta K. Panigrahi
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Group Velocity Dispersion ◽  
Experimental Parameter ◽  
Traveling Wave Solutions ◽  
Equation Model ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Dark Solitons

We investigate exact traveling wave solutions of higher order nonlinear Schrödinger equation (NLSE) in the absence of third-order dispersion, which exhibit nontrivial self-phase modulation. It is shown that the corresponding dynamical equation, governing the evolution of intensity in the femtosecond regime, is that of NLSE with a source. The exact localized solutions to this system can have both super and subluminal propagation belonging to two distinct classes. A number of these solitons exhibit chirality, thereby showing preferential propagation behavior determined by group velocity dispersion. Both localized bright and dark solitons are found in complementary velocity and experimental parameter domains, which can exist for anomalous and normal dispersion regimes. It is found that dark solitons in this system propagate with nonzero velocity, unlike their counterpart in nanosecond regime. Interestingly, subluminal propagation is observed for solitons having a nontrivial Padé type intensity profile.

Resonant optical solitons with conformable time-fractional nonlinear Schrödinger equation

2020 ◽  
pp. 2150044
Author(s):  
Aly R. Seadawy ◽  
M. Bilal ◽  
M. Younis ◽  
S. T. R. Rizvi
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Group Velocity Dispersion ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Kerr Nonlinearity ◽  
Nonlinear Schrodinger Equation ◽  
Hyperbolic Function ◽  
Nonlinear Schrödinger

We successfully apply extended rational sine-cosine/sinh-cosh and advance expansion function techniques in this paper. Various kinds of soliton solutions to the conformable time-fractional resonant nonlinear Schrödinger equation (RNLSE) in optical fiber are extracted. We discuss the system with the effects of coefficients like group velocity dispersion, non-Kerr nonlinearity, resonant nonlinearity, and construct optical soliton solution in terms of rational, trigonometric and hyperbolic function solutions with arbitrary parameters. The recovered solutions reveal that the applied approaches are straightforward and efficient to work out the excellent contribution for analyzing several classes of nonlinear partial differential equations (NLPDEs) in engineering and sciences. Moreover, 3D, 2D and contour graphs are sketched with suitable selection of the parameters under the criteria of constraints conditions.

Optical solitons and stability analysis for the generalized second-order nonlinear Schrödinger equation in an optical fiber

2020 ◽  
Vol 21 (7-8) ◽  
pp. 855-863 ◽  
Author(s):  
Nauman Raza ◽  
Saima Arshed ◽  
Ahmad Javid
Keyword(s):  
Stability Analysis ◽  
Schrödinger Equation ◽  
Optical Fiber ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Expansion Method ◽  
Optical Solitons ◽  
Nonlinear Schrodinger Equation ◽  
Second Order ◽  
Nonlinear Schrödinger

AbstractIn this paper, the generalized second-order nonlinear Schrödinger equation with light-wave promulgation in an optical fiber, is studied for optical soliton solutions. Three analytical methods such as the $\mathrm{exp}\left(-\phi \left(\chi \right)\right)$-expansion method, the G′/G2-expansion method and the first integral methods are used to extract dark, singular, periodic, dark-singular combo optical solitons for the proposed model. These solitons appear with constraint conditions on their parameters and they are also presented. These three strategic schemes have made this retrieval successful. The given model is also studied for modulation instability on the basis of linear stability analysis. A dispersion relation is obtained between wave number and frequency.

scholarly journals Second order averaging for the nonlinear Schrödinger equation with strongly anisotropic potential

2011 ◽  
Vol 4 (4) ◽  
pp. 831-856 ◽  
Author(s):  
Naoufel Ben Abdallah ◽  
◽  
Yongyong Cai ◽  
Francois Castella ◽  
Florian Méhats ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Second Order ◽  
Nonlinear Schrödinger
Sign in / Sign up

Export Citation Format

Share Document