Darboux Transformation and N-Soliton Solution for the Coupled Modified Nonlinear Schrödinger Equations

2012 ◽  
Vol 67 (12) ◽  
pp. 711-722 ◽  
Author(s):  
Hai-Qiang Zhang
Keyword(s):  
Optical Fibers ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Pulse Propagation ◽  
Integrable Model ◽  
Transformation Method ◽  
Coupled Equations ◽  
Exchange Collision ◽  
Potential Applications ◽  
Zero Potential

The pulse propagation in the picosecond or femtosecond regime of birefringent optical fibers is governed by the coupled mixed derivative nonlinear Schr¨odinger (CMDNLS) equations. A new type of Lax pair associated with such coupled equations is derived from the Wadati-Konno-Ichikawa spectral problem. The Darboux transformation method is applied to this integrable model, and the N-times iteration formula of the Darboux transformation is presented in terms of the compact determinant representation. Starting from the zero potential, the bright vector N-soliton solution of CMDNLS equations is expressed as a compact determinant by N complex eigenvalues and N linearly independent eigenfunctions. The collision mechanisms in two components shows that bright vector solitons can exhibit the standard elastic and inelastic collisions. Such energy-exchange collision behaviours have potential applications in the construction of logical gates, the design of fiber directional couplers, and quantum information processors.

SOLITON PROPAGATION IN NONUNIFORM OPTICAL FIBERS

2003 ◽  
Vol 12 (03) ◽  
pp. 341-348 ◽  
Author(s):  
YAN XIAO ◽  
ZHIYONG XU ◽  
LU LI ◽  
ZHONGHAO LI ◽  
GUOSHENG ZHOU
Keyword(s):  
Optical Fibers ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Transmission System ◽  
Soliton Propagation ◽  
Soliton Transmission System ◽  
Soliton Transmission

In this paper, we construct the Lax pair for a soliton transmission system in nonuniform optical fibers and give N-soliton solution using the Darboux transformation. The explicit one-soliton and two-soliton solutions are presented. Further, we discuss the interaction scenario between two neighboring solitons and the effect of the inhomogeneities of the fiber (z0) on the interaction between two neighboring solitons.

Simulations of pulse propagation in optical fibers using graphics processor units

2011 ◽  
Vol 182 (7) ◽  
pp. 1414-1420 ◽  
Author(s):  
J.M. Alcaraz-Pelegrina ◽  
P. Rodríguez-García
Keyword(s):  
Optical Fibers ◽  
Pulse Propagation ◽  
Graphics Processor

Laser pulse propagation in optical fibers as destroying factor where outer local thermal actions apply

2001 ◽  
Author(s):  
Vladimir A. Burdin ◽  
Alexey V. Voronkov ◽  
Alexander N. Platonov ◽  
Andrew V. Balobanov
Keyword(s):  
Laser Pulse ◽  
Optical Fibers ◽  
Pulse Propagation

Analytical simulations of the Fokas system; extension (2 + 1)-dimensional nonlinear Schrödinger equation

2021 ◽  
Author(s):  
Mostafa M. A. Khater
Keyword(s):  
Optical Fibers ◽  
Pulse Propagation ◽  
Dynamical Behavior ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Contour Plots ◽  
System Extension ◽  
Inverse Spectral Method ◽  
Nonlinear Pulse Propagation ◽  
The Stability

This paper studies novel analytical solutions of the extended [Formula: see text]-dimensional nonlinear Schrödinger (NLS) equation which is also known with [Formula: see text]-dimensional complex Fokas ([Formula: see text]D–CF) system. Fokas derived this system in 1994 by using the inverse spectral method. This model is considered as an icon model for nonlinear pulse propagation in monomode optical fibers. Many novel computational solutions are constructed through two recent analytical schemes (Ansatz and Projective Riccati expansion (PRE) methods). These solutions are represented through sketches in 2D, 3D, and contour plots to demonstrate the dynamical behavior of pulse propagation in breather, rogue, periodic, lump, and solitary characteristics. The stability property of the obtained solutions is examined based on the Hamiltonian system’s properties. The obtained solutions are checked by putting them back into the original equation through Mathematica 12 software.

scholarly journals Infiltrated Photonic Crystal Fibers for Sensing Applications

Sensors ◽  
2018 ◽  
Vol 18 (12) ◽  
pp. 4263 ◽  
Author(s):  
José Algorri ◽  
Dimitrios Zografopoulos ◽  
Alberto Tapetado ◽  
David Poudereux ◽  
José Sánchez-Pena
Keyword(s):  
Photonic Crystal ◽  
Optical Fibers ◽  
Photonic Crystal Fibers ◽  
Scale Up ◽  
Dispersion Parameters ◽  
Power Pulse ◽  
Sensing Applications ◽  
Potential Applications ◽  
Crystal Fibers ◽  
Bose Einstein

Photonic crystal fibers (PCFs) are a special class of optical fibers with a periodic arrangement of microstructured holes located in the fiber’s cladding. Light confinement is achieved by means of either index-guiding, or the photonic bandgap effect in a low-index core. Ever since PCFs were first demonstrated in 1995, their special characteristics, such as potentially high birefringence, very small or high nonlinearity, low propagation losses, and controllable dispersion parameters, have rendered them unique for many applications, such as sensors, high-power pulse transmission, and biomedical studies. When the holes of PCFs are filled with solids, liquids or gases, unprecedented opportunities for applications emerge. These include, but are not limited in, supercontinuum generation, propulsion of atoms through a hollow fiber core, fiber-loaded Bose–Einstein condensates, as well as enhanced sensing and measurement devices. For this reason, infiltrated PCF have been the focus of intensive research in recent years. In this review, the fundamentals and fabrication of PCF infiltrated with different materials are discussed. In addition, potential applications of infiltrated PCF sensors are reviewed, identifying the challenges and limitations to scale up and commercialize this novel technology.

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].

Mixed interaction solutions for the coupled nonlinear Schrödinger equations

2021 ◽  
pp. 2150004
Author(s):  
Yaning Tang ◽  
Jiale Zhou
Keyword(s):  
Darboux Transformation ◽  
Rogue Waves ◽  
Transformation Method ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Interaction Solutions ◽  
Nonlinear Schrodinger Equations

We investigate the mixed interaction solutions of the coupled nonlinear Schrödinger equations (CNLSE) through the Darboux transformation method. First of all, we derive the nonsingular localized wave solutions for two cases of CNLSE by the Darboux transformation method and matrix analysis method. Furthermore, we take a limit technique to deduce rogue waves and divide the rogue waves into four categories through analyzing their dynamic behaviors. Based on the obtained theorems, the Darboux transformations are presented to solve interaction solutions between distinct nonlinear waves. In this paper, we mainly study four types. Finally, the dynamic characteristics of the constructed these solutions are analyzed by sequences of interesting figures plotted with the help of Maple.

scholarly journals Suspended-Core Microstructured Polymer Optical Fibers and Potential Applications in Sensing

Sensors ◽  
2019 ◽  
Vol 19 (16) ◽  
pp. 3449 ◽  
Author(s):  
Wanvisa Talataisong ◽  
Rand Ismaeel ◽  
Martynas Beresna ◽  
Gilberto Brambilla
Keyword(s):  
Optical Fibers ◽  
Material Selection ◽  
Biological Species ◽  
Single Step ◽  
3D Printer ◽  
Sensing Applications ◽  
Wide Range ◽  
Potential Applications ◽  
Pressure Chemical ◽  
Polymer Optical Fibers

The study of the fabrication, material selection, and properties of microstructured polymer optical fibers (MPOFs) has long attracted great interest. This ever-increasing interest is due to their wide range of applications, mainly in sensing, including temperature, pressure, chemical, and biological species. This manuscript reviews the manufacturing of MPOFs, including the most recent single-step process involving extrusion from a modified 3D printer. MPOFs sensing applications are then discussed, with a stress on the benefit of using polymers.

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