Optical soliton and weierstrass elliptic function management to parabolic law nonlinear directional couplers and modulation instability spectra

2021 ◽  
Vol 53 (8) ◽  
Author(s):  
Alphonse Houwe ◽  
Souleymanou Abbagari ◽  
Savaissou Nestor ◽  
Mustafa Inc ◽  
Mir Sajjad Hashemi ◽  
...  
Keyword(s):  
Elliptic Function ◽  
Modulation Instability ◽  
Optical Soliton ◽  
Directional Couplers ◽  
Weierstrass Elliptic Function ◽  
Parabolic Law ◽  
Function Management

scholarly journals Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical Fibers

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 219
Author(s):  
Khalil S. Al-Ghafri
Keyword(s):  
Differential Equation ◽  
Optical Fibers ◽  
Power Law ◽  
Elliptic Function ◽  
Landau Equation ◽  
Soliton Solutions ◽  
Space Time ◽  
Optical Soliton ◽  
Ginzburg Landau ◽  
Weierstrass Elliptic Function

In this work, we investigate the conformable space–time fractional complex Ginzburg–Landau (GL) equation dominated by three types of nonlinear effects. These types of nonlinearity include Kerr law, power law, and dual-power law. The symmetry case in the GL equation due to the three types of nonlinearity is presented. The governing model is dealt with by a straightforward mathematical technique, where the fractional differential equation is reduced to a first-order nonlinear ordinary differential equation with solution expressed in the form of the Weierstrass elliptic function. The relation between the Weierstrass elliptic function and hyperbolic functions enables us to derive two types of optical soliton solutions, namely, bright and singular solitons. Restrictions for the validity of the optical soliton solutions are given. To shed light on the behaviour of solitons, the graphical illustrations of obtained solutions are represented for different values of various parameters. The symmetrical structure of some extracted solitons is deduced when the fractional derivative parameters for space and time are symmetric.

Optical soliton to multi-core (coupling with all the neighbors) directional couplers and modulation instability

2021 ◽  
Vol 136 (3) ◽  
Author(s):  
Souleymanou Abbagari ◽  
Alphonse Houwe ◽  
Hadi Rezazadeh ◽  
Ahmet Bekir ◽  
Thomas Bouetou Bouetou ◽  
...  
Keyword(s):  
Modulation Instability ◽  
Optical Soliton ◽  
Directional Couplers

scholarly journals Optical soliton perturbation in parabolic law medium having weak non-local nonlinearity by a couple of strategic integration architectures

2019 ◽  
Vol 13 ◽  
pp. 102334 ◽  
Author(s):  
Anjan Biswas ◽  
Yakup Yıldırım ◽  
Emrullah Yaşar ◽  
Qin Zhou ◽  
Ali Saleh Alshomrani ◽  
...  
Keyword(s):  
Optical Soliton ◽  
Strategic Integration ◽  
Soliton Perturbation ◽  
Parabolic Law ◽  
Non Local ◽  
Local Nonlinearity

scholarly journals Simultaneous approximation of et and ℘(t)

1982 ◽  
Vol 33 (2) ◽  
pp. 171-178
Author(s):  
K. Saradha
Keyword(s):  
Complex Number ◽  
Elliptic Function ◽  
Simultaneous Approximation ◽  
Algebraic Numbers ◽  
Weierstrass Elliptic Function ◽  
Algebraic Invariants ◽  
Image Position

AbstractLet t be any complex number different from the poles of a Weierstrass elliptic function ℘(z), having algebraic invariants. Then we estimate from below the sum where α and β are algebraic numbers. The estimate is given in terms of the heights of α and β and the degree of the field Q(α, β), where Q is the field of rationals.

Application of the Weierstrass Elliptic Expansion Method to the Long-Wave and Short-Wave Resonance Interaction System

2008 ◽  
Vol 63 (5-6) ◽  
pp. 273-279 ◽  
Author(s):  
Xian-Jing Lai ◽  
Jie-Fang Zhang ◽  
Shan-Hai Mei
Keyword(s):  
Periodic Solutions ◽  
Elliptic Function ◽  
Expansion Method ◽  
Short Wave ◽  
Resonance Interaction ◽  
Solitary Wave Solutions ◽  
Jacobian Elliptic Function ◽  
Weierstrass Elliptic Function ◽  
Long Wave ◽  
Wave Resonance

With the aid of symbolic computation, nine families of new doubly periodic solutions are obtained for the (2+1)-dimensional long-wave and short-wave resonance interaction (LSRI) system in terms of the Weierstrass elliptic function method. Moreover Jacobian elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.

A METHOD TO CONSTRUCT WEIERSTRASS ELLIPTIC FUNCTION SOLUTION FOR NONLINEAR EQUATIONS

2011 ◽  
Vol 25 (14) ◽  
pp. 1931-1939 ◽  
Author(s):  
LIANG-MA SHI ◽  
LING-FENG ZHANG ◽  
HAO MENG ◽  
HONG-WEI ZHAO ◽  
SHI-PING ZHOU
Keyword(s):  
Nonlinear Equations ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Order Derivative ◽  
First Order ◽  
Function Solution ◽  
Weierstrass Elliptic Function ◽  
Klein Gordon

A method for constructing the solutions of nonlinear evolution equations by using the Weierstrass elliptic function and its first-order derivative was presented. This technique was then applied to Burgers and Klein–Gordon equations which showed its efficiency and validality for exactly some solving nonlinear evolution equations.

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