Fractional Propagation of Short Light Pulses in Monomode Optical Fibers: Comparison of Beta Derivative and Truncated M- Fractional Derivative

2021 ◽  
Author(s):  
Muhammad Bilal Riaz ◽  
Adil Jhangeer ◽  
Jan Awrejcewicz ◽  
Dumitru Baleanu ◽  
Sana Tahir
Keyword(s):  
Fractional Derivative ◽  
Fiber Optics ◽  
Optical Fibers ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
The Other ◽  
Light Pulses ◽  
Free Parameters ◽  
Fractional Orders ◽  
Algebraic Technique

Abstract The present study is dedicated to the computation and analysis of solitonic structures of a nonlinear Sasa-Satsuma equation that comes in handy to understand the propagation of short light pulses in the monomode fiber optics with the aid of Beta Derivative and Truncated M- fractional derivative. We employ new direct algebraic technique for nonlinear Sasa-Satsuma equation to derive novel soliton solutions. A variety of soliton solutions are retrieved in trigonometric, hyperbolic, exponential, rational forms. The vast majority of obtained solutions represent the lead of this method on other techniques. The prime advantage of considered technique over the other techniques is that it provides more diverse solutions with some free parameters. Moreover, the fractional behavior of the obtained solutions is analyzed thoroughly by using two and three dimensional graphs. Which shows that for lower fractional orders i.e $\beta=0.1$, the magnitude of truncated M-fractional derivative is greater whereas for increasing fractional orders i.e $\beta=0.7$ and $\beta=0.99$, magnitude remains same for both definitions except for a phase shift in some spatial domain that eventually vanishes and two curves coincide.

Dynamics of optical solitons incorporating Kerr dispersion and self-frequency shift

2019 ◽  
Vol 33 (19) ◽  
pp. 1950220
Author(s):  
Asma Rashid Butt ◽  
Muhammad Abdullah ◽  
Nauman Raza
Keyword(s):  
Frequency Shift ◽  
Optical Fibers ◽  
Laser Light ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Optical Solitons ◽  
Light Pulses ◽  
Ode Method ◽  
Analytical Approaches ◽  
Extended Trial

This paper deals with the dynamics of optical solitons in nonlinear Schrödinger equation (NLSE) with cubic-quintic law nonlinearity in the presence of self-frequency shift and self-steepening. This type of equation describes the ultralarge capacity transmission and traveling of laser light pulses in optical fibers. Two robust analytical approaches are employed to determine contemporary solutions. Some new explicit rational, periodic and combo periodic soliton solutions are extracted using the extended trial equation method. The Riccati–Bernoulli sub-ODE method provided us with singular and dark soliton solutions. The constraints found are necessary for the existence of solitons.

Construction of optical soliton solutions of the generalized nonlinear Radhakrishnan–Kundu–Lakshmanan dynamical equation with power law nonlinearity

2020 ◽  
Vol 34 (13) ◽  
pp. 2050139 ◽  
Author(s):  
Aly R. Seadawy ◽  
Sultan Z. Alamri ◽  
Haya M. Al-Sharari
Keyword(s):  
Optical Fibers ◽  
Dynamical Equation ◽  
Physical Phenomenon ◽  
Soliton Solutions ◽  
Optical Soliton ◽  
Solitary Wave Solutions ◽  
Light Pulses ◽  
Wave Solutions ◽  
Different Types ◽  
Modified Simple Equation Method

The propagation of soliton through optical fibers has been studied by using nonlinear Schrödinger’s equation (NLSE). There are different types of NLSEs that study this physical phenomenon such as (GRKLE) generalized Radhakrishnan–Kundu–Lakshmanan equation. The generalized nonlinear RKL dynamical equation, which presents description of the dynamical of light pulses, has been studied. We used two formulas of the modified simple equation method to construct the optical soliton solutions of this model. The obtained solutions can be represented as bistable bright, dark, periodic solitary wave solutions.

Optical soliton solutions for nonlinear complex Ginzburg–Landau dynamical equation with laws of nonlinearity Kerr law media

2020 ◽  
Vol 34 (19) ◽  
pp. 2050179
Author(s):  
Aly R. Seadawy ◽  
Mujahid Iqbal
Keyword(s):  
Fiber Optics ◽  
Optical Fibers ◽  
Landau Equation ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Power Laws ◽  
Optical Soliton ◽  
Quantum Plasma ◽  
Ginzburg Landau ◽  
Soliton Dynamics

In this research article, our aim is to construct new optical soliton solutions for nonlinear complex Ginzburg–Landau equation with the help of modified mathematical technique. In this work, we studied both laws of nonlinearity (Kerr and power laws). The obtained solutions represent dark and bright solitons, singular and combined bright-dark solitons, traveling wave, and periodic solitary wave. The determined solutions provide help in the development of optical fibers, soliton dynamics, and nonlinear optics. The constructed solitonic solutions prove that the applicable technique is more reliable, efficient, fruitful and powerful to investigate higher order complex nonlinear partial differential equations (PDEs) involved in mathematical physics, quantum plasma, geophysics, mechanics, fiber optics, field of engineering, and many other kinds of applied sciences.

Optical dark and singular solitons of generalized nonlinear Schrödinger’s equation with anti-cubic law of nonlinearity

2019 ◽  
Vol 33 (13) ◽  
pp. 1950158 ◽  
Author(s):  
Nauman Raza ◽  
Asad Zubair
Keyword(s):  
Optical Fibers ◽  
Soliton Solutions ◽  
Algebraic Method ◽  
Rational Solutions ◽  
Schrödinger’S Equation ◽  
Light Pulses ◽  
Propagation Of Light ◽  
Schrödinger's Equation ◽  
Nonlinear Schrodinger’S Equation ◽  
Nonlinear Schrödinger’S Equation

This work is devoted to scrutinize new optical soliton solutions to the spatially temporal [Formula: see text]-dimensional nonlinear Schrödinger’s equation (NLSE) with anti-cubic nonlinearity. Two different versatile integration architectures are used to extract these solitons. Extended direct algebraic method (EDAM) is utilized to pluck out optical, dark and singular soliton solutions, whereas generalized Kudryashov method (GKM) provides rational solutions. The fetched results are new and useful for the propagation of light pulses in optical fibers in [Formula: see text]-dimensions. For the existence of these solitons, constraint conditions are also listed.

scholarly journals Exact optical solitons of the perturbed nonlinear Schrödinger–Hirota equation with Kerr law nonlinearity in nonlinear fiber optics

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 526-534 ◽  
Author(s):  
Alphonse Houwe ◽  
Souleymanou Abbagari ◽  
Gambo Betchewe ◽  
Mustafa Inc ◽  
Serge Y. Doka ◽  
...  
Keyword(s):  
Fiber Optics ◽  
Optical Fibers ◽  
Soliton Solutions ◽  
Auxiliary Equation ◽  
Coupling Coefficients ◽  
Hirota Equation ◽  
Auxiliary Equation Method ◽  
Nonlinear Schrödinger ◽  
Kerr Law Nonlinearity ◽  
Constraint Relation

AbstractThis article studies dark, bright, trigonometric and rational optical soliton solutions to the perturbed nonlinear Schrödinger–Hirota equation (PNLSHE). Hence, we have examined two cases: first, restrictions have been done to the third-order (TOD) (γ) as constraint relation, and the coupling coefficients (σ) is obtained as well as the velocity of the soliton by adopting the traveling wave hypothesis. Second, the TOD and the coupling coefficients are non-zero value, sending back to the PNLSHE, which has been studied in refs. [4,10,16] recently. By employing two relevant integration technics such as the auxiliary equation and the modified auxiliary equation method, miscellaneous optical solitary wave is obtianed, which is in agreement with the outcomes collected by the previous studies [4,16]. These results help in obtaining nonlinear optical fibers in the future.

Tomography of Optical Emission Line Intensities of a Radio-Frequency Magnetron Discharge

1997 ◽  
Vol 51 (9) ◽  
pp. 1340-1345 ◽  
Author(s):  
F. Debal ◽  
M. Wautelet ◽  
J. P. Dauchot ◽  
M. Hecq
Keyword(s):  
Radio Frequency ◽  
Fiber Optics ◽  
Optical Fibers ◽  
Optical Tomography ◽  
Three Dimensional ◽  
Optical Emission ◽  
Ccd Camera ◽  
Experimental Setup ◽  
Mathematical Function ◽  
Magnetron Discharge

An experimental setup for spectroscopic optical tomography of glow discharges is presented. It combines a fiber-optics system with a monochromator coupled to a charge-coupled device (CCD) camera. The light emitted by the discharge is sent to the input of 10 optical fibers through a collimating system. The outputs of these optical fibers are coupled to the entrance slit of a monochromator. The CCD camera is in the output slit. This arrangement allowed us to acquire 10 spectra simultaneously, each being associated with a small zone of the discharge. By translation of the optical fibers, the whole discharge was studied. The data were then analyzed by means of a tomographic reconstruction program in order to obtain the three-dimensional spectroscopic optical tomography, for a large number of lines. This experimental setup was used to deduce the three-dimensional optical emission of various lines of a radio-frequency (rf)-powered magnetron discharge. The discharge deals with an aluminum base alloy cathode, sputtered by Ar. Emission lines corresponding to the cathode (Al: 394.4- and 396.2-nm lines) and the gas discharge (Ar: 763.5 nm-line) were considered. The three-dimensional emission profiles, I( r, Z), of the lines were measured; r is the distance from the center of the cathode, and Z is the distance from the cathode. I( r, Z) profiles are different for the Al and Ar lines. The effects of the electrical power and the pressure were also studied. It was found that the corresponding I( r, Z) profiles behave differently with the pressure. In order to compare the results, I( r, Z) was fitted with an empirical analytical mathematical function, with parameters depending on pressure. At high pressure, the shape of I( r, Z) for the Al line tends towards the shape of the Ar line.

Generalization of optical solitons with dual dispersion in the presence of Kerr and quadratic-cubic law nonlinearities

2019 ◽  
Vol 33 (01) ◽  
pp. 1850427 ◽  
Author(s):  
Nauman Raza ◽  
Ahmad Javid
Keyword(s):  
Fiber Optics ◽  
Group Velocity Dispersion ◽  
Soliton Solutions ◽  
Optical Solitons ◽  
Light Pulses ◽  
Cubic Law ◽  
Propagation Of Light ◽  
Spatio Temporal ◽  
Modified Simple Equation Method ◽  
Temporal Dispersion

In this work, nonlinear Schrödinger’s equation along with group velocity dispersion and spatio-temporal dispersion is considered in [Formula: see text] dimensions with Kerr and quadratic-cubic law nonlinearities which expose the propagation of light pulses in fiber optics. Dark, singular and periodic singular optical solitons in [Formula: see text] dimensions are retrieved and generalized through versatile modified simple equation method. The constraint conditions that righteously guarantee the perseverance of these soliton solutions are obtained as an outgrowth. The results presented in this paper are new and generalized which are already available in the literature.

Three-Dimensional Reconstruction of Two Forms of the Chaperonin GRO EL

1990 ◽  
Vol 48 (1) ◽  
pp. 258-259
Author(s):  
J.L. Carrascosa ◽  
G. Abella ◽  
S. Marco ◽  
M. Muyal ◽  
J.M. Carazo
Keyword(s):  
Three Dimensional ◽  
The Other ◽  
Two Dimensional ◽  
Series Method ◽  
Three Dimensional Reconstruction ◽  
Structural Components ◽  
E Coli ◽  
Dimensional Reconstruction ◽  
Morphogenetic Factors ◽  
Tilt Series

Chaperonins are a class of proteins characterized by their role as morphogenetic factors. They trantsiently interact with the structural components of certain biological aggregates (viruses, enzymes etc), promoting their correct folding, assembly and, eventually transport. The groEL factor from E. coli is a conspicuous member of the chaperonins, as it promotes the assembly and morphogenesis of bacterial oligomers and/viral structures.We have studied groEL-like factors from two different bacteria:E. coli and B.subtilis. These factors share common morphological features , showing two different views: one is 6-fold, while the other shows 7 morphological units. There is also a correlation between the presence of a dominant 6-fold view and the fact of both bacteria been grown at low temperature (32°C), while the 7-fold is the main view at higher temperatures (42°C). As the two-dimensional projections of groEL were difficult to interprete, we studied their three-dimensional reconstruction by the random conical tilt series method from negatively stained particles.

An Efficient Multiple Description Coding for Multi-View Video Based on the Correlation of Spatial Polyphase Transformed Subsequences

2019 ◽  
Vol 63 (5) ◽  
pp. 50401-1-50401-7 ◽  
Author(s):  
Jing Chen ◽  
Jie Liao ◽  
Huanqiang Zeng ◽  
Canhui Cai ◽  
Kai-Kuang Ma
Keyword(s):  
Video Transmission ◽  
Video Sequence ◽  
Three Dimensional ◽  
The Other ◽  
Multiple Description Coding ◽  
Multiple Description ◽  
Prediction Mode ◽  
Gradient Based ◽  
Directional Interpolation ◽  
Description Coding

Abstract For a robust three-dimensional video transmission through error prone channels, an efficient multiple description coding for multi-view video based on the correlation of spatial polyphase transformed subsequences (CSPT_MDC_MVC) is proposed in this article. The input multi-view video sequence is first separated into four subsequences by spatial polyphase transform and then grouped into two descriptions. With the correlation of macroblocks in corresponding subsequence positions, these subsequences should not be coded in completely the same way. In each description, one subsequence is directly coded by the Joint Multi-view Video Coding (JMVC) encoder and the other subsequence is classified into four sets. According to the classification, the indirectly coding subsequence selectively employed the prediction mode and the prediction vector of the counter directly coding subsequence, which reduces the bitrate consumption and the coding complexity of multiple description coding for multi-view video. On the decoder side, the gradient-based directional interpolation is employed to improve the side reconstructed quality. The effectiveness and robustness of the proposed algorithm is verified by experiments in the JMVC coding platform.

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

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