Complex model ultra-short pulses in optical fibers via generalized third-order nonlinear Schrödinger dynamical equation

2020 ◽  
Vol 34 (17) ◽  
pp. 2050143
Author(s):  
Aly R. Seadawy ◽  
Naila Nasreen ◽  
Dianchen Lu
Keyword(s):  
Optical Fibers ◽  
Three Dimensional ◽  
Current Method ◽  
Dark Soliton ◽  
Complex Model ◽  
Contour Plot ◽  
Dynamical Equations ◽  
Third Order ◽  
Short Pulses ◽  
Nonlinear Schrödinger

In this paper, several types of solitons such as dark soliton, bright soliton, periodic soliton, kink soliton and solitary waves in three-dimensional and two-dimensional contour plot have been derived for the generalized third-order nonlinear Schrödinger dynamical equations (NLSEs). The generalized third-order NLSE is a significant model ultra-short pulses in optical fibers. The computational work and outcomes achieved show the influence and efficiency of current method. Furthermore, we can solve many other higher-order NLSEs with the help of simple and effective technique.

Non-Linear Dynamic Stability of Shallow Reticulated Spherical Shells

2011 ◽  
Vol 142 ◽  
pp. 107-110
Author(s):  
Ming Jun Han ◽  
You Tang Li ◽  
Ping Qiu ◽  
Xin Zhi Wang
Keyword(s):  
Three Dimensional ◽  
Dynamical Equations ◽  
Third Order ◽  
Spherical Shells ◽  
Nonlinear Dynamical ◽  
Linear Dynamic ◽  
The Third ◽  
Displacement Mode ◽  
Nonlinear Forced Vibration ◽  
The Stability

The nonlinear dynamical equations are established by using the method of quasi-shells for three-dimensional shallow spherical shells with circular bottom. Displacement mode that meets the boundary conditions of fixed edges is given by using the method of the separate variable, A nonlinear forced vibration equation containing the second and the third order is derived by using the method of Galerkin. The stability of the equilibrium point is studied by using the Floquet exponent.

Breathers and double-pole solutions of coupled mixed derivative nonlinear Schrödinger equations from optical fibers

2021 ◽  
pp. 2150373
Author(s):  
Chen Hang ◽  
Qing-Lin Wu ◽  
Hai-Qiang Zhang
Keyword(s):  
Optical Fibers ◽  
Dark Soliton ◽  
Nonlinear Schrödinger Equations ◽  
Mixed Derivative ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Double Pole ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Wave Numbers

In this paper, the coupled mixed derivative nonlinear Schrödinger equations are investigated, which govern the propagation of the femtosecond optical pulse in optical fibers. First of all, based on the soliton solutions in bilinear form, the breathers are constructed by choosing a pair of complex conjugate wave numbers. Then, the interactions between a breather and either an anti-dark soliton or a dark soliton are studied according to the existence conditions of dark and anti-dark solitons. The double-pole solution can also be obtained by a coalescence of two wave numbers. In addition, the influence of physical parameters on the phases and propagation direction of the breathers and double-pole solitons is studied by the qualitative analysis and graphical illustration.

Three-Dimensional Bright–Dark Soliton, Bright Soliton Pairs, and Rogue Wave of Coupled Nonlinear Schr¨odinger Equation with Time–Space Modulation

2012 ◽  
Vol 67 (8-9) ◽  
pp. 483-490 ◽  
Author(s):  
Junchao Chen ◽  
Biao Li
Keyword(s):  
Similarity Transformation ◽  
Rogue Wave ◽  
Three Dimensional ◽  
Dark Soliton ◽  
Variable Coefficients ◽  
Nonlinear Schrödinger ◽  
Time Space ◽  
Potential Applications ◽  
Constant Coefficients ◽  
Space Modulation

We systematically provide a similarity transformation reducing the (3+1)-dimensional inhomogeneous coupled nonlinear Schrodinger (CNLS) equation with variable coefficients and parabolic potential to the (1+1)-dimensional coupled nonlinear Schrodinger equation with constant coefficients. Based on the similarity transformation, we discuss the dynamics of the propagation of the three-dimensional bright-dark soliton, the interaction between two bright solitons, and the feature of the three-dimensional rogue wave with different parameters. The obtained results may raise the possibility of relative experiments and potential applications.

N-dark–dark solitons for the coupled higher-order nonlinear Schrödinger equations in optical fibers

2017 ◽  
Vol 31 (33) ◽  
pp. 1750305 ◽  
Author(s):  
Hai-Qiang Zhang ◽  
Yue Wang
Keyword(s):  
Optical Fibers ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Higher Order ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Dark Solitons ◽  
Nonlinear Schrodinger Equations

In this paper, we construct the binary Darboux transformation on the coupled higher-order dispersive nonlinear Schrödinger equations in optical fibers. We present the N-fold iterative transformation in terms of the determinants. By the limit technique, we derive the N-dark–dark soliton solutions from the non-vanishing background. Based on the obtained solutions, we find that the collision mechanisms of dark vector solitons exhibit the standard elastic collisions in both two components.

Non-Linear Dynamic Characteristics of Single-Layer Shallow Reticulated Spherical Shells

2013 ◽  
Vol 303-306 ◽  
pp. 2794-2797
Author(s):  
Zhen Yang ◽  
Yu Lian Chen ◽  
Ming Jun Han
Keyword(s):  
Three Dimensional ◽  
Single Layer ◽  
Dynamical Equations ◽  
Third Order ◽  
Spherical Shells ◽  
Nonlinear Dynamical ◽  
Floquet Exponent ◽  
Displacement Mode ◽  
Nonlinear Forced Vibration ◽  
The Stability

The nonlinear dynamical equations are established by using the method of quasi-shells for three-dimensional shallow spherical shells with circular bottom. Displacement mode that meets the boundary conditions of fixed edges is given by using the method of the separate variable, A nonlinear forced vibration equation containing the second and the third order is derived by using the method of Galerkin. The stability of the equilibrium point is studied by using the Floquet exponent.

scholarly journals 3D Unsteady Diffusion and Reaction-Diffusion with Singularities by GFEM with 27-Node Hexahedrons

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Estaner Claro Romão
Keyword(s):  
Finite Element ◽  
Variable Temperature ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Third Order ◽  
Order Of Accuracy ◽  
Finite Element Approximations ◽  
Temperature Solution ◽  
The One ◽  
Primary Variable

The Galerkin Finite Element Method (GFEM) with 8- and 27-node hexahedrons elements is used for solving diffusion and transient three-dimensional reaction-diffusion with singularities. Besides analyzing the results from the primary variable (temperature), the finite element approximations were used to find the derivative of the temperature in all three directions. This technique does not provide an order of accuracy compatible with the one found in the temperature solution; thereto, a calculation from the third order finite differences is proposed here, which provide the best results, as demonstrated by the first two applications proposed in this paper. Lastly, the presentation and the discussion of a real application with two cases of boundary conditions with singularities are proposed.

Experimental Observation of the Fundamental Dark Soliton in Optical Fibers

1988 ◽  
Vol 61 (21) ◽  
pp. 2445-2448 ◽  
Author(s):  
A. M. Weiner ◽  
J. P. Heritage ◽  
R. J. Hawkins ◽  
R. N. Thurston ◽  
E. M. Kirschner ◽  
...  
Keyword(s):  
Experimental Observation ◽  
Optical Fibers ◽  
Dark Soliton
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