Compression of optical similaritons induced by cubic-quintic nonlinear media in a graded-index waveguide

2016 ◽  
Vol 25 (03) ◽  
pp. 1650033 ◽  
Author(s):  
Ritu Pal ◽  
Amit Goyal ◽  
Shally Loomba ◽  
Thokala Soloman Raju ◽  
C. N. Kumar
Keyword(s):  
Variable Coefficient ◽  
Free Parameter ◽  
Propagation Distance ◽  
Nonlinearity Coefficient ◽  
Cubic Nonlinearity ◽  
Nonlinear Media ◽  
Graded Index ◽  
Double Kink ◽  
Quintic Nonlinear Schrödinger Equation ◽  
Similarity Reductions

We employ the similarity reductions in two steps to obtain a family of bright and dark similaritons for the variable coefficient cubic–quintic nonlinear Schrödinger equation. Also, parameter domains are delineated in which kink and double-kink similaritons exist for this model. This methodology introduces a free parameter through cubic nonlinearity coefficient which gives us freedom to tune the amplitude and the propagation distance of similaritons in a tapered graded-index waveguide. Furthermore, we observe rapid beam compression of these similaritons for varying detuning parameter and the coefficient of cubic nonlinearity.

Stable high dimensional solitons in nonlocal competing cubic-quintic nonlinear media

2021 ◽  
Author(s):  
Qiying Zhou ◽  
Hui-jun Li
Keyword(s):  
Propagation Constant ◽  
Nonlinear Coefficient ◽  
High Dimensional ◽  
Cubic Nonlinearity ◽  
Nonlinear Media ◽  
Nonlinear Modes ◽  
Quintic Nonlinearity ◽  
The Stability

Abstract We find and stabilize high dimensional dipole and quadrupole solitons in nonlocal competing cubic-quintic nonlinear media. By adjusting the propagation constant, cubic and quintic nonlinear coefficients, the stable intervals for dipole and quadrupole solitons which are parallel to $x$ axis and ones after rotating 45 degrees counterclockwise around the origin of coordinate are found. For the dipole solitons and ones after rotating, their stability is controlled by the propagation constant, the coefficients of cubic and quintic nonlinearity. For the quadrupole solitons, their stability is controlled by the propagation constant and the coefficient of cubic nonlinearity, rather than the coefficient of quintic nonlinearity, though there is a small effect of the quintic nonlinear coefficient on the stability. Our proposal may provide a way to generate and stabilize some novel high dimensional nonlinear modes in nonlocal system.

A variable coefficient nonlinear Schrödinger equation: localized waves on the plane wave background and their dynamics

2019 ◽  
Vol 33 (10) ◽  
pp. 1850121 ◽  
Author(s):  
Xiu-Bin Wang ◽  
Bo Han
Keyword(s):  
Variable Coefficient ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Rational Solutions ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Plane Wave Background ◽  
Localized Waves ◽  
Similarity Reductions

In this work, a variable coefficient nonlinear Schrödinger (vc-NLS) equation is under investigation, which can describe the amplification or absorption of pulses propagating in an optical fiber with distributed dispersion and nonlinearity. By means of similarity reductions, a similar transformation helps us to relate certain class of solutions of the standard NLS equation to the solutions of integrable vc-NLS equation. Furthermore, we analytically consider nonautonomous breather wave, rogue wave solutions and their interactions in the vc-NLS equation, which possess complicated wave propagation in time and differ from the usual breather waves and rogue waves. Finally, the main characteristics of the rational solutions are graphically discussed. The parameters in the solutions can be used to control the shape, amplitude and scale of the rogue waves.

Dark–dark and bright–dark solitons for a (2+1)-dimensional variable-coefficient nonlinear Schrödinger system in a graded-index waveguide

2020 ◽  
Vol 34 (17) ◽  
pp. 2050183
Author(s):  
Jie Zhang ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
Yu-Qiang Yuan ◽  
He-Yuan Tian ◽  
...  
Keyword(s):  
Variable Coefficient ◽  
Soliton Solutions ◽  
Beam Width ◽  
Dark Soliton ◽  
Nonlinear Schrödinger ◽  
Graded Index ◽  
Dark Solitons ◽  
Nonlinear Schrödinger System ◽  
Dimensional Variable ◽  
Schrödinger System

In this letter, we study a (2[Formula: see text]+[Formula: see text]1)-dimensional variable-coefficient nonlinear Schrödinger system, which describes an optical beam inside the two-dimensional graded-index waveguide with polarization effects. Through the Kadomtsev–Petviashvili hierarchy reduction, the [Formula: see text] dark–dark soliton and [Formula: see text] bright-dark soliton solutions in terms of the Gramian are obtained, where [Formula: see text] is a positive integer. We analyze the interaction and propagation of the dark–dark solitons graphically. With the different values of the diffraction coefficient [Formula: see text], periodic-, cubic- and parabolic-shaped dark–dark solitons are derived. With the different values of the gain/loss coefficient [Formula: see text], periodic- and arctangent-profile background waves are obtained. Moreover, we discuss the effects from the dimensionless beam width [Formula: see text], [Formula: see text] and [Formula: see text] on the solitons and background waves: Shapes of the solitons are affected by [Formula: see text] and [Formula: see text], while profiles of the background waves are affected by [Formula: see text] and [Formula: see text].

An analytical method for soliton solutions of perturbed Schrödinger’s equation with quadratic-cubic nonlinearity

2019 ◽  
Vol 33 (03) ◽  
pp. 1950018 ◽  
Author(s):  
Behzad Ghanbari ◽  
Nauman Raza
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Cubic Nonlinearity ◽  
Nonlinear Media ◽  
Schrödinger’S Equation ◽  
Wave Solutions ◽  
First Time ◽  
Schrödinger's Equation

In this study, we acquire some new exact traveling wave solutions to the nonlinear Schrödinger’s equation in the presence of Hamiltonian perturbations. The compendious integration tool, generalized exponential rational function method (GERFM), is utilized in the presence of quadratic-cubic nonlinear media. The obtained results depict the efficiency of the proposed scheme and are being reported for the first time.

Spatial solitons in a medium with lumped amplification and dissipation

2015 ◽  
Vol 24 (01) ◽  
pp. 1550011 ◽  
Author(s):  
K. Aysha Muhsina ◽  
P. A. Subha
Keyword(s):  
Propagation Distance ◽  
Spatial Soliton ◽  
Amplification Coefficient ◽  
Kerr Medium ◽  
Two Dimensional ◽  
Spatial Solitons ◽  
Linear Amplification ◽  
Graded Index ◽  
Kerr Media ◽  
Soliton Dynamics

This work analyzes the dynamics of two-dimensional spatial solitons in dissipative graded index Kerr media, analytically and numerically. The dynamics of two-dimensional spatial solitons has been studied in a medium with lumped amplification. The presence of lumped amplification in the medium results in the formation of soliton like waves called similaritons. The spatial soliton dynamics has been studied in a dissipative medium. In a dissipative graded index Kerr medium, the balancing between the coefficients of constant dissipation and lumped amplification results in the stabilization of the beam. The beam dynamics has also been studied by varying amplification coefficients with propagation distance. Hyperbolic, linear, and exponential amplification profiles are considered. When amplification coefficient varies with propagation distance, the beam gets compressed. The beam compression is higher in the case of exponential amplification profile than that of hyperbolic and linear amplification profiles.

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