On pulse propagation of soliton wave solutions related to the perturbed Chen–Lee–Liu equation in an optical fiber

2021 ◽  
Vol 53 (10) ◽  
Author(s):  
Haci Mehmet Baskonus ◽  
M. S. Osman ◽  
Hamood ur Rehman ◽  
Muhammad Ramzan ◽  
Muhammad Tahir ◽  
...  
Keyword(s):  
Optical Fiber ◽  
Pulse Propagation ◽  
Wave Solutions ◽  
Soliton Wave Solutions

scholarly journals Optical solutions and other solutions for Radhakrishnan-Kundu-Laksmannan equation by using improved modified extended tanh-function method

2021 ◽  
Author(s):  
Ahmed M. Elsherbeny ◽  
Reda El–Barkouky ◽  
Hamdy Ahmed ◽  
Rabab M. I. El-Hassani ◽  
Ahmed H. Arnous
Keyword(s):  
Optical Fiber ◽  
Function Method ◽  
Pulse Propagation ◽  
Periodic Wave ◽  
Optical Fiber Communications ◽  
Periodic Wave Solutions ◽  
Bright Solitons ◽  
Wave Solutions ◽  
Elliptic Solutions ◽  
Fiber Communications

Abstract This paper studies Radhakrishnan-Kundu-Laksmannan equation which is used to describe the pulse propagation in optical fiber communications. By using improved modified extended tanh-function method various types of solutions are extracted such as bright solitons, singular solitons, singular periodic wave solutions, Jacobi elliptic solutions, periodic wave solutions and Weierstrass elliptic doubly periodic solutions. Moreover, some of the obtained solutions are represented graphically.

scholarly journals Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber

2019 ◽  
Vol 53 (1) ◽  
pp. 87-107
Author(s):  
Felipe Alexander Pipicano ◽  
Juan Carlos Muñoz Grajales
Keyword(s):  
Hamiltonian System ◽  
Optical Fiber ◽  
Numerical Simulations ◽  
Standing Wave ◽  
Kerr Effect ◽  
Wave Equations ◽  
Pulse Propagation ◽  
Standing Waves ◽  
Wave Solutions ◽  
Periodic Standing Waves

We establish existence of periodic standing waves for a model to describe the propagation of a light pulse inside an optical fiber taking into account the Kerr effect. To this end, we apply the Lyapunov Center Theorem taking advantage that the corresponding standing wave equations can be rewritten as a Hamiltonian system. Furthermore, some of these solutions are approximated by using a Newton-type iteration, combined with a collocation-spectral strategy to discretize the system of standing wave equations. Our numerical simulations are found to be in accordance with our analytical results.

Analytical new soliton wave solutions of the nonlinear conformable time-fractional coupled Whitham–Broer–Kaup equations

2021 ◽  
pp. 2150492
Author(s):  
Delmar Sherriffe ◽  
Diptiranjan Behera ◽  
P. Nagarani
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Function Method ◽  
Visual Representations ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Varying Parameters ◽  
Wave Solutions ◽  
Soliton Wave Solutions

The study of nonlinear physical and abstract systems is greatly important in order to determine the behavior of the solutions for Fractional Partial Differential Equations (FPDEs). In this paper, we study the analytical wave solutions of the time-fractional coupled Whitham–Broer–Kaup (WBK) equations under the meaning of conformal fractional derivative. These solutions are derived using the modified extended tanh-function method. Accordingly, different new forms of the solutions are obtained. In order to understand its behavior under varying parameters, we give the visual representations of all the solutions. Finally, the graphs are discussed and a conclusion is given.

scholarly journals ANALYSIS OF ULTRA-SHORT PULSE PROPAGATION IN NONLINEAR OPTICAL FIBER

2009 ◽  
Vol 12 ◽  
pp. 219-241 ◽  
Author(s):  
Mohamed Bakry El Mashade ◽  
Mohamed Nady Abdel Aleem
Keyword(s):  
Optical Fiber ◽  
Nonlinear Optical ◽  
Pulse Propagation ◽  
Short Pulse ◽  
Ultra Short Pulse

Bifurcations and Exact Traveling Wave Solutions for a Model of Nonlinear Pulse Propagation in Optical Fibers

2014 ◽  
Vol 24 (06) ◽  
pp. 1450088
Author(s):  
Jibin Li
Keyword(s):  
Optical Fibers ◽  
Traveling Wave ◽  
Pulse Propagation ◽  
Dynamical Behavior ◽  
Traveling Wave Solutions ◽  
Wave System ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Nonlinear Pulse Propagation

In this paper, we consider a model of nonlinear pulse propagation in optical fibers. By investigating the dynamical behavior and bifurcations of solutions of the traveling wave system of PDE, we derive all possible exact explicit traveling wave solutions under different parameter conditions. These results completed the study of traveling wave solutions for the mentioned model posed by [Lenells, 2009].

Multiple rogue and soliton wave solutions to the generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation arising in fluid mechanics and plasma physics

2021 ◽  
pp. 2150383
Author(s):  
Onur Alp Ilhan ◽  
Sadiq Taha Abdulazeez ◽  
Jalil Manafian ◽  
Hooshmand Azizi ◽  
Subhiya M. Zeynalli
Keyword(s):  
Rogue Wave ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
The Novel ◽  
Algebraic Equations ◽  
Bilinear Method ◽  
Dynamical Characteristics ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Soliton Wave Solutions

Under investigation in this paper is the generalized Konopelchenko–Dubrovsky–Kaup-Kupershmidt equation. Based on bilinear method, the multiple rogue wave (RW) solutions and the novel multiple soliton solutions are constructed by giving some specific activation functions for the considered model. By means of symbolic computation, these analytical solutions and corresponding rogue wave solutions are obtained via Maple 18 software. The exact lump and RW solutions, by solving the under-determined nonlinear system of algebraic equations for the specified parameters, will be constructed. Via various three-dimensional plots and density plots, dynamical characteristics of these waves are exhibited.

Lump soliton wave solutions for the (2+1)-dimensional Konopelchenko–Dubrovsky equation and KdV equation

2019 ◽  
Vol 33 (18) ◽  
pp. 1950199 ◽  
Author(s):  
Mostafa M. A. Khater ◽  
Dianchen Lu ◽  
Raghda A. M. Attia
Keyword(s):  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Auxiliary Equation ◽  
Wave Solutions ◽  
All Solutions ◽  
Long Range Interactions ◽  
Weak Scattering ◽  
Novel Method ◽  
Soliton Wave Solutions

This paper studies (2+1)-dimensional Konopelchenko–Dubrovsky equation and (2+1)-dimensional KdV equation via a modified auxiliary equation technique. These two systems describe the connection between the nonlinear weaves with a weak scattering and long-range interactions between the tropical, mid-latitude troposphere, the interaction of equatorial and mid-latitude Rossby waves, respectively. We implement a novel technique to these systems to find analytical traveling wave solutions. The performance of this novel method shows its ability for applying on various nonlinear partial differential equations. All solutions obtained are checked by the Maple software system and verified for its high fidelity.

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