The higher-order nonlinear Schrödinger’s dynamical equation with fourth-order dispersion and cubic-quintic nonlinearity via dispersive analytical soliton wave solutions

2021 ◽  
Vol 53 (12) ◽  
Author(s):  
Wafaa B. Rabie ◽  
Hamdy M. Ahmed ◽  
Aly R. Seadawy ◽  
Ali Althobaiti
Keyword(s):  
Fourth Order ◽  
Dynamical Equation ◽  
Higher Order ◽  
Quintic Nonlinearity ◽  
Wave Solutions ◽  
Soliton Wave Solutions ◽  
Order Dispersion

Analytical methods via bright–dark solitons and solitary wave solutions of the higher-order nonlinear Schrödinger equation with fourth-order dispersion

2019 ◽  
Vol 33 (35) ◽  
pp. 1950443 ◽  
Author(s):  
Aly R. Seadawy ◽  
Mujahid Iqbal ◽  
Dianchen Lu
Keyword(s):  
Solitary Wave ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Solitary Wave Solutions ◽  
Physical Sciences ◽  
Dark Solitons ◽  
Wave Solutions ◽  
Order Dispersion

In this research work, we investigated the higher-order nonlinear Schrödinger equation (NLSE) with fourth-order dispersion, self-steepening, nonlinearity, nonlinear dispersive terms and cubic-quintic terms which is described as the propagation of ultra-short pulses in fiber optics. We apply the modification form of extended auxiliary equation mapping method to find the new exact and solitary wave solutions of higher-order NLSE. As a result, new solutions are obtained in the form of solitons, kink–anti-kink type solitons, bright–dark solitons, traveling wave, trigonometric functions, elliptic functions and periodic solitary wave solutions. These new different types of solutions show the power and fruitfulness of this new method and also show two- and three-dimensional graphically with the help of computer software Mathematica. These new solutions have many applications in the field of physics and other branches of physical sciences. We can also solve other higher-order nonlinear partial differential equations (NPDEs) involved in mathematical physics and other various branches of physical sciences with this new technique.

scholarly journals Influence of Even-Order Dispersion on Super-Sech Soliton Transmission Quality under Coherent Crosstalk

2008 ◽  
Vol 2008 ◽  
pp. 1-5 ◽  
Author(s):  
Aleksandra Panajotovic ◽  
Daniela Milovic ◽  
Anjan Biswas ◽  
Essaid Zerrad
Keyword(s):  
Fourth Order ◽  
Optical Network ◽  
Single Mode ◽  
Single Mode Fiber ◽  
Higher Order ◽  
Trailing Edges ◽  
Even Order ◽  
Transmission Quality ◽  
The Impact ◽  
Order Dispersion

The transmission speed of optical network strongly depends on the impact of higher order dispersion. In presence of coherent crosstalk, which cannot be otherwise controlled by optical filtering, the impact of higher order dispersions becomes more pronounced. In this paper, the general expressions, that describe pulse deformation due to second- and fourth-order dispersions in a single-mode fiber, are given. The responses for such even-order dispersions, in presence of coherent crosstalk, are characterized by waveforms with long trailing edges. The transmission quality of optical pulses, due to both individual and combined influence of second- and fourth-order dispersions, is studied in this paper. Finally, the pulse shape and eye diagrams are obtained.

Modulational Instability of the Higher-Order Nonlinear Schrödinger Equation with Fourth-Order Dispersion and Quintic Nonlinear Terms

2006 ◽  
Vol 61 (5-6) ◽  
pp. 225-234 ◽  
Author(s):  
Woo-Pyo Hong
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Modulational Instability ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Normal Dispersion ◽  
Nonlinear Schrödinger ◽  
Order Dispersion

The modulational instability of the higher-order nonlinear Schrödinger equation with fourth-order dispersion and quintic nonlinear terms, describing the propagation of extremely short pulses, is investigated. Several types of gains by modulational instability are shown to exist in both the anomalous and normal dispersion regimes depending on the sign and strength of the higher-order nonlinear terms. The evolution of the modulational instability in both the anomalous and normal dispersion regimes is numerically investigated and the effects of the higher-order dispersion and nonlinear terms on the formation and evolution of the solitons induced by modulational instability are studied. - PACS numbers: 42.65.Tg, 42.81Dp, 42.65Sf

Perturbation of higher-order solitons by fourth-order dispersion in optical fibers

2009 ◽  
Vol 282 (18) ◽  
pp. 3798-3803 ◽  
Author(s):  
Samudra Roy ◽  
Shyamal K. Bhadra ◽  
Govind P. Agrawal
Keyword(s):  
Optical Fibers ◽  
Fourth Order ◽  
Higher Order ◽  
Order Dispersion

scholarly journals New exact soliton solutions, bifurcation and multistability behaviors of traveling waves for the (3+1)-dimensional modified Zakharov-Kuznetsov equation with higher order dispersion

2021 ◽  
Author(s):  
Asit Saha ◽  
Battal Gazi Karakoç ◽  
Khalid K. Ali
Keyword(s):  
Traveling Wave ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Higher Order ◽  
Physical Parameters ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Higher Order Dispersion ◽  
Order Dispersion ◽  
Bifurcation Behavior

The goal of the present paper is to obtain and analyze new exact travelling wave solutions and bifurcation behavior of modified Zakharov-Kuznetsov (mZK) equation with higher order dispersion term. For this purpose, first and second simple methods are used to build soliton solutions of travelling wave solutions. Furthermore, bifurcation behavior of traveling waves including new type of quasiperiodic and multi-periodic traveling wave motions have been examined depending on the physical parameters. Multistability for the nonlinear mZK equation has been investigated depending on fixed values of physical parameters with various initial conditions. The suggested methods for the analytical solutions are powerful and benefical tools to obtain the exact travelling wave solutions of nonlinear evolution equations (NLEEs). Two and three-dimensional plots are also provided to illustrate the new solutions. Bifurcation and multistability behaviors of traveling wave solution of the nonlinear mZK equation with higher order dispersion will add some value in the literature of mathematical and plasma physics.

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