Gray Solitons Research Articles

Chirped gray and singular optical solitons with generalized quadratic-cubic law of self-phase modulation and nonlinear chromatic dispersion

Chirped gray and singular optical solitons with generalized quadratic-cubic law of self-phase modulation and nonlinear chromatic dispersion

Saturation and absorption effects on the transmission properties of Kerr-type nonlinear layers

The effects of absorption and saturation on soliton states in Kerr-type nonlinear layers are theoretically investigated. In addition to the usual gray and bright soliton structures observed in nonlinear slabs, a flat soliton, i.e., a particular soliton excitation with electric field amplitude independent of the position within the layer, is researched in cases of self-defocusing and self-focusing nonlinearities. Effects caused by the combination of absorption and saturation, such as the shift and extinction of the flat soliton peak, the decrease in the amplitude of the electric field within the nonlinear layer, and the suppression of the multistable behavior of the transmission coefficient in the vicinity of the soliton peaks, are discussed. The present theoretical results are compared and found in good quantitative agreement with previous experimental measurements.Graphical

Envelope solitary waves in two-negative ions with stationary dust grains

Using a multi-fluid model, we look at how modulated electrostatic dust-ion-acoustic wave packets move nonlinearly through a plasma made up of a three-ion fluid with Maxwellian electrons and stationary dust grains. A nonlinear Schrödinger (NLS) equation describes the electric potential envelope wave packet. The analysis reveals the existence of different types of localized modes, namely bright, dark, and grey solitons. We numerically analyse the coefficients of the NLS equation to identify stable or unstable regions for wave packet propagation. It is found that higher relative density ratios increase the group velocity of the wave packets. Stable pulses can become unstable when plasma parameters exceed certain relative density ratio values. Stable pulses can exist within a crucial window of the relative dust density ratio. Controlling the dust grain density ratio outside the zone can cause unstable wave packets or bright envelope solitons to propagate.

Propagation properties and stability of dark solitons in weakly interacting Bose–Bose droplets

We investigate dark solitons in two-component Bose systems with competing interactions in one dimension. Such a system hosts a liquid phase stabilized by the beyond-mean field corrections. Using the generalized Gross–Pitaevskii equation, we reveal the presence of two families of solitonic solutions. The solitons in both of them can be engineered to be arbitrarily wide. One family of solutions, however, has an anomalous dispersion relation, and our analyses show one of its branches is unstable. We find a critical velocity that demarcates the stable from unstable solutions. Nonetheless, gray anomalous solitons can exist inside quantum droplets and can be treated as solitonic excitations thereof.

Effect of κ-deformed Kaniadakis distribution on the modulational instability of electron-acoustic waves in a non-Maxwellian plasma

In this paper, the modulational instability (MI) of the high-frequency electron-acoustic waves (EAWs) is reported in a non-Maxwellian plasma composed of two distinct types of electrons and stationary ions. One type of electrons is treated as a cold inertial fluid, whereas the other type is considered as inertialess species following κ-deformed Kaniadakis distribution. The fluid equations to the current model are reduced via a reductive perturbation technique to a nonlinear Schrödinger equation, which is then used to compute the MI and the growth rate of the EAWs. It is instructive to note that the deformation parameter (which develops the Kaniadakis entropy) and the hot-to-cold electron density ratio (hot electron concentration) significantly affect the conditions for MI. The modulated envelope black (dark and gray) solitons are investigated. The current results are beneficial in analyzing the spectrum of the cosmic rays, which violates manifestly the Boltzmann–Gibbs statistics. Moreover, the obtained results can be used to understand the mystery of many observations in stars where the presence of non-Maxwellian particles dominates.

Interactions and Dynamics of One-Dimensional Droplets, Bubbles and Kinks

We explore the dynamics and interactions of multiple bright droplets and bubbles, as well as the interactions of kinks with droplets and with antikinks, in the extended one-dimensional Gross–Pitaevskii model including the Lee–Huang–Yang correction. Existence regions are identified for the one-dimensional droplets and bubbles in terms of their chemical potential, verifying the stability of the droplets and exposing the instability of the bubbles. The limiting case of the droplet family is a stable kink. The interactions between droplets demonstrate in-phase (out-of-phase) attraction (repulsion), with the so-called Manton’s method explicating the observed dynamical response, and mixed behavior for intermediate values of the phase shift. Droplets bearing different chemical potentials experience mass-exchange phenomena. Individual bubbles exhibit core expansion and mutual attraction prior to their destabilization. Droplets interacting with kinks are absorbed by them, a process accompanied by the emission of dispersive shock waves and gray solitons. Kink–antikink interactions are repulsive, generating counter-propagating shock waves. Our findings reveal dynamical features of droplets and kinks that can be detected in current experiments.

New exact solutions of optical metamaterial model with the Kerr law nonlinearity

This paper deals with the investigation of the newly obtained solitary solutions of perturbed optical metamaterial with Kerr law nonlinearity. Two novel analytical techniques, namely, the extended Riccati equation rational expansion (ERERE) method and the extended rational [Formula: see text]-expansion (EREE) methods are applied to develop new solitary solutions. The resultant wave solutions are periodic wave solution, singular kink, anti-peakon, dark, singular anti-kink, anti-kink, gray and singular soliton solutions. The detailed dynamics of the retrieved solutions are the most potent influence of the proposed methods which shows the efficacy and fruitfulness of both the methods.

Dynamics of polaron formation in 1D Bose gases in the strong-coupling regime

We discuss the dynamics of the formation of a Bose polaron when an impurity is injected into a weakly interacting one-dimensional Bose condensate. While for small impurity-boson couplings this process can be described within the Froehlich model as generation, emission and binding of Bogoliubov phonons, this is no longer adequate if the coupling becomes strong. To treat this regime we consider a mean-field approach beyond the Froehlich model which accounts for the backaction to the condensate, complemented with Truncated Wigner simulations to include quantum fluctuation. For the stationary polaron we find a periodic energy-momentum relation and non-monotonous relation between impurity velocity and polaron momentum including regions of negative impurity velocity. Studying the polaron formation after turning on the impurity-boson coupling quasi-adiabatically and in a sudden quench, we find a very rich scenario of dynamical regimes. Due to the build-up of an effective mass, the impurity is slowed down even if its initial velocity is below the Landau critical value. For larger initial velocities we find deceleration and even backscattering caused by emission of density waves or grey solitons and subsequent formation of stationary polaron states in different momentum sectors. In order to analyze the effect of quantum fluctuations we consider a trapped condensate to avoid 1D infrared divergencies. Using Truncated Wigner simulations in this case we show under what conditions the influence of quantum fluctuations is small.

Fate of the vacuum point and of gray solitons in dispersive quantum shock waves in a one-dimensional Bose gas

Fate of the vacuum point and of gray solitons in dispersive quantum shock waves in a one-dimensional Bose gas

Solitary waves in a quantum droplet-bearing system

We unravel the existence and stability properties of dark soliton solutions as they extend from the regime of trapped quantum droplets towards the Thomas-Fermi limit in homonuclear symmetric Bose mixtures. Leveraging a phase-plane analysis, we identify the regimes of existence of different types of quantum droplets and subsequently examine the possibility of black and gray solitons and kink-type structures in this system. Moreover, we employ the Landau dynamics approach to extract an analytical estimate of the oscillation frequency of a single dark soliton in the relevant extended Gross--Pitaevskii model. Within this framework, we also find that the single soliton immersed in a droplet is stable, while multisoliton configurations exhibit parametric windows of oscillatory instabilities. Our results pave the way for studying dynamical features of nonlinear multisoliton excitations in a droplet environment in contemporary experimental settings.

Grey-Black Optical Solitons, Homoclinic Breather, Combined Solitons via Chupin Liu’s Theorem for Improved Perturbed NLSE with Dual-Power Law Nonlinearity

In this article, we consider the improved perturbed nonlinear Schrödinger Equation (IP-NLSE) with dual power law nonlinearity, which arises in optical fibers and photovoltaic-photo-refractive materials. We found grey and black optical solitons of the governing equation by means of a suitable complex envelope ansatz solution. By using the Chupin Liu’s theorem (CLT) for the grey and black solitons, we evaluated new categories of combined optical soliton (COS) solutions to the IP-NLSE. The propagation behaviors for homoclinic breathers (HB), multiwaves and M-shape solitons will be analytically examined. All new analytical solutions will be found by an ansatz function scheme and suitable transformations. Multiwave solitons have been reported by using a three-waves technique. Furthermore, two kinds of interactions for M-shape soliton through exponential functions will be examined.

Propagation of chirped gray solitons in weakly nonlocal media with parabolic law nonlinearity and spatio-temporal dispersion

In our research, we have examined the existence and stability of chirped periodic and solitary waves in a weakly nonlocal nonlinear medium, which exhibits various types of effects, including inter-modal dispersion, nonlinear dispersion, detuning, spatio-temporal, and parabolic law nonlinearity. By studying the nonlinear Schrödinger equation that describes the field dynamics in this system, a class of nonlinearly chirped periodic waves is derived in the presence of all physical processes. In addition, we have obtained solitary waves of the gray type in the long-wave limit of these nonlinear waveforms. We have found that the frequency chirp associated with these optical waves depends on their intensity and its magnitude can be controlled by manipulating the nonlinear dispersion parameter. Furthermore, we have numerically studied the stability of the gray soliton solution under finite initial perturbations. Our results indicate that the nonlinear waves we have identified represent new types of extremely robust chirped localized structures in weakly nonlocal nonlinear parabolic law media.

The beam control in two-channels PT-symmetric waveguide with fractional diffraction effect

The double gray solitons and beams control in two-channels PT-symmetric waveguide with fractional diffraction are studied. In the defocusing Kerr nonlinear effect, the stable double gray solitons can be obtained in the two-channels PT-symmetric waveguide. The effects of Lévy index and gain/loss coefficient on the existence, stability, gray scale and power of gray solitons are studied in detail. In addition, the transmission and control of bright soliton beams are studied in the two-channels PT-symmetric waveguide with focusing Kerr nonlinear effect. Due to the refractive index distribution of waveguide, the beam propagates as a respirator along the center when it inputs from the center. Otherwise, the propagation of beam occurs oscillation between two channels. The input positions and Lévy index can affect the frequency and amplitude of beam oscillation. And the gain/loss coefficient can cause energy flowing. Double beams can occur periodic elastic collisions and form a peak wave in the waveguide.

Bifurcation of backward and forward solitary waves in helicoidal Peyrard–Bishop–Dauxois model of DNA

In this work, we investigate the bifurcation of backward and forward solitary waves in helicoidal Peyrard–Bishop–Dauxois model of deoxyribonucleic acid (DNA). We start by showing that this model can adopt right-handed or left-handed behavior depending on the wave frequency that it propagates. Then, using the semi-discrete approximation, we show that the dynamics of modulated waves in the network is governed by a quintic nonlinear Schrödinger (QNLS). Applying the phase imprint technique, this QNLS equation is first reduced into a derivative QNLS, and then to a cubic–quintic Duffing oscillator equation. Based on the phase plane analysis, we present all phase portraits of the dynamical system. The obtained results show a number of new phase portraits which cannot exist without the phase imprint approach. The exact representations of the nonlinear localized waves corresponding to the homoclinic and heteroclinic orbits in the phase portrait of the dynamical system are given. These waves include bright soliton, kink and anti-kink solitons, dark soliton and grey solitons. In addition, the effects of phase imprint parameter on the wave-shape profile of these solutions are investigated. We find out that the phase imprint parameter considerably affects the amplitude and the width of each of the above enumerated solitary waves, while the phase imprint method leads to new type solutions.

Chirped spatial solitons on a continuous-wave background in weak nonlocal media with polynomial law of nonlinearity

Spatial soliton propagation in a cubic-quintic-septimal optical material with a weakly nonlocal response is examined. We demonstrate that bright and gray solitons on a continuous-wave background exist for the envelope equation describing their dynamis in the physical media. In addition, optical kink and anti-kink type solitons are also identified. We find that these waveforms exhibit a frequency chirping property which is inversely proportional to the beam intensity. A noteworthy characteristic is that the chirped soliton solutions include no free parameters and their properties such as their amplitude, spatial width and propagation constant are determined solely by the material parameters. The numerical examples are structured for illustrating the propagation dynamics of these solitons in the optical system. The role of weak nonlocality on the modulation instability gain has also been discussed.

Higher dimensional reciprocal integrable Kaup-Newell systems

The study of integrable systems is one of important topics both in physics and in mathematics. However, traditional studies on integrable systems are usually restricted in (1+1) and (2+1) dimensions. The main reasons come from the fact that high-dimensional integrable systems are extremely rare. Recently, we found that a large number of high dimensional integrable systems can be derived from low dimensional ones by means of a deformation algorithm. In this paper, the (1+1) dimensional Kaup-Newell (KN) system is extended to a (4+1) dimensional system with the help of the deformation algorithm. In addition to the original (1+1) dimensional KN system, the new system also contains three reciprocal forms of the (1+1) dimensional KN system. The model also contains a large number of new (<i>D</i>+1) dimensional (<inline-formula><tex-math id="M2">\begin{document}$D \leqslant 3$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222418_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222418_M2.png"/></alternatives></inline-formula>) integrable systems. The Lax integrability and symmetry integrability of the (4+1) dimensional KN system are also proved. It is very difficult to solve the new high-dimensional KN systems. In this paper, we only investigate the traveling wave solutions of a (2+1) dimensional reciprocal derivative nonlinear Schrödinger equation. The general envelope travelling wave can be expressed by a complicated elliptic integral. The single envelope dark (gray) soliton of the derivative nonlinear Schödinger equation can be implicitly written.

Darboux transformation, localized waves and conservation laws for an [formula omitted]-coupled variable-coefficient nonlinear Schrödinger system in an inhomogeneous optical fiber

Optical fiber communication system is one of the supporting systems in the modern internet age. We investigate an M-coupled variable-coefficient nonlinear Schrödinger system, which describes the simultaneous pulse propagation of the M-field components in an inhomogeneous optical fiber, where M is a positive integer. With respect to the complex amplitude of the jth-field (j=1,…,M) component in the optical fiber, we construct an n-fold Darboux transformation, where n is a positive integer. Based on the n-fold Darboux transformation, we obtain some one- and two-fold localized wave solutions for the above system with the mixed defocusing-focusing-type nonlinearity and M=2. We acquire the infinitely-many conservation laws. Via such solutions, we obtain some vector gray solitons, interactions between the two vector parabolic/cubic gray solitons, and interactions between the vector parabolic/cubic breathers and gray solitons with different β(z), γ(z) and δ(z), the coefficients of the group velocity dispersion, nonlinearity and amplification/absorption. It can be found that δ(z) affects the backgrounds of the breathers and gray solitons.

Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity

We present exact numerical data for the lowest-energy momentum eigenstates (yrast states) of a repulsive spin impurity in a one-dimensional Bose gas using full configuration interaction quantum Monte Carlo (FCIQMC). As a stochastic extension of exact diagonalization, it is well suited for the study of yrast states of a lattice-renormalized model for a quantum gas. Yrast states carry valuable information about the dynamic properties of slow-moving mobile impurities immersed in a many-body system. Based on the energies and the first and second-order correlation functions of yrast states, we identify different dynamical regimes and the transitions between them: The polaron regime, where the impurity’s motion is affected by the Bose gas through a renormalized effective mass; a regime of a gray soliton that is weakly correlated with a stationary impurity, and the depleton regime, where the impurity occupies a dark or gray soliton. Extracting the depleton effective mass reveals a super heavy regime where the magnitude of the (negative) depleton mass exceeds the mass of the finite Bose gas.

Coupled mode and novel soliton structure in fused coupler

In this paper, we investigate the characteristics of bright-like solitons, flat-topped solitons, and gray solitons in nonlocal nonlinear fused coupler. Firstly, the fundamental bright-like solitons with different parameters are obtained by the Newton iteration. It is found that the peak value and beam width of the ground state bright-like soliton increase with the enhancement of the nonlocality degree and nonlinear parameter, and they decrease with the propagation constant increasing. The power of the ground state bright-like soliton increases with the increase of the nonlocality degree and the width of coupling function, and it decreases with the propagation constant increasing. These numerical results can also be verified in the case of multipolar bright-like solitons. Secondly, by changing the coupled mode, the solutions of multipolar bright-like solitons, flat-topped soliton and grey solitons are obtained. The transmission stability of multipolar bright-like solitons, flat-topped soliton and grey solitons are studied. The stability of solitons is verified by means of linear stability analysis and fractional Fourier evolution. In the process of long-distance propagation, the propagation of bright-like solitons, gray solitons, and flat-topped soliton with one to three-pole symmetric peaks are stable, and the tripolar bright-like solitons with different soliton peaks and tripolar gray solitons are unable to transmit steadily. At the same time, it is found that the gray soliton with three poles or more is not easy to maintain its transmission stability. It is also found that the higher the grey scale of the gray soliton, the easier it is to realize stable transmission. Finally, it is found that the coupling function width not only affects the power of the soliton, but also realize the conversion among different soliton structures by adjusting the coupling function width.

Grey solitons in the ultracold fermions at the full spin polarization

A minimal coupling quantum hydrodynamic model of spin-1/2 fermions at the full spin polarization corresponding to a nonlinear Schrodinger equation is considered. The nonlinearity is primarily caused by the Fermi pressure. It provides an effective repulsion between fermions. However, there is the additional contribution of the short-range interaction appearing in the third order by the interaction radius. It leads to the modification of the pressure contribution. Solitons are considered for the infinite medium with no restriction on the amplitude of the wave. The Fermi pressure leads to the soliton in form of the area of decreased concentration. However, the center of solution corresponding to the area of minimal concentration has nonzero value of concentration. Therefore, the grey soliton is found. Soliton exist if the speed of its propagation is below the Fermi velocity. Keywords: degenerate fermions, hydrodynamics, non-linear Schrodinger equation, dark soliton, Fermi pressure.