Properties Of Solitons Research Articles

Oscillatory dissipative solitons stabilized by nonlinear gradient terms: The transition to localized spatiotemporal disorder.

We investigate properties of oscillatory dissipative solitons (DSs) in a cubic complex Ginzburg-Landau equation stabilized by nonlinear gradient terms. As a main result we find a transition to dissipative solitons with spatiotemporal disorder as a function of the diffusion coefficient. This transition proceeds via quasiperiodicity and shows incommensurate satellites next to the fundamental frequency and its harmonics indicating a possible route to localized spatiotemporal chaos. The transition back to oscillatory DSs follows a similar scenario.

Plasma Shock Wave in Gamma-Ray Bursts: Nonlinear Phenomena and Radiative Process

Since gamma-ray bursts (GRBs) are related to extreme explosions in the universe, they provide a unique setup to study various space plasma phenomena. The GRB spectra supply a wide range of information regarding the various nonlinear interactions and associated structures. In this work, we study the generation of shock fronts and their properties in a plasma. Such a plasma shock is the aftereffect of an explosion of which the prompt emission of GRBs are the signatures. The shock fronts are studied analytically by deriving the KdV–Burger’s equation. The solution of the KdV–Burgers equation via the “Cole-Hoff transformation” is studied alongside the usual “hyperbolic-tangent method.” The dynamical properties of the shock solitons are studied further to second our findings and find the stability and any possibility of chaos. The results will help to interpret the stellar plasma properties from data. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PACS</i> —95.30.Qd, 52.65.-y, 52.35.-g, 52.35.Tc, 52.27.Lw

The Korteweg-de Vries–Caudrey–Dodd–Gibbon dynamical model: Its conservation laws, solitons, and complexiton

The main purpose of the present paper is to conduct a detailed and thorough study on the Korteweg-de Vries–Caudrey–Dodd–Gibbon (KdV-CDG) dynamical model. More precisely, after considering the integrable KdV-CDG dynamical model describing certain properties of ocean dynamics, its conservation laws, solitons, and complexiton are respectively derived using the Ibragimov, Kudryashov, and Hirota methods. Several numerical simulations in two and three-dimensional postures are formally given to analyze the effect of nonlinear parameters. It is shown that nonlinear parameters play a key role in the dynamical properties of soliton and complexiton solutions.

Stability of Algebraic Solitons for Nonlinear Schrödinger Equations of Derivative Type: Variational Approach

We consider the following nonlinear Schr\"{o}dinger equation of derivative type: \begin{equation} i \partial_t u + \partial_x^2 u +i |u|^{2} \partial_x u +b|u|^4u=0 , \quad (t,x) \in \mathbb{R}\times\mathbb{R}, \ b \in \mathbb{R}. \end{equation} If $b=0$, this equation is a gauge equivalent form of well-known derivative nonlinear Schr\"{o}dinger (DNLS) equation. The soliton profile of the DNLS equation satisfies a certain double power elliptic equation with cubic-quintic nonlinearities. The quintic nonlinearity in the equation only affects the coefficient in front of the quintic term in the elliptic equation, so the additional nonlinearity is natural as a perturbation preserving soliton profiles of the DNLS equation. If $b>-\frac{3}{16}$, the equation has algebraic solitons as well as exponentially decaying solitons. In this paper we study stability properties of solitons by variational approach, and prove that if $b<0$, all solitons including algebraic solitons are stable in the energy space. The existence of stable algebraic solitons shows an interesting mathematical example because stable algebraic solitons are not known in the context of the corresponding double power NLS.

Charge self-trapping in two strand biomolecules: Adiabatic polaron approach

We investigate the properties of the excess charge (electron, hole) introduced into a two-strand biomolecule. We consider the possibility that the stable soliton excitation can be formed due to interaction of excess charge with the phonon subsystem. The influence of overlap of the molecular orbitals between adjacent structure elements of the macromolecular chain on the soliton properties is discussed. Special attention is paid to the influence of the overlapping of the molecular orbitals between structure elements placed on the different chains. Using the literature values of the basic energy parameters of the two-chain biomolecular structures, possible types of soliton solutions are discussed.

Interaction properties of double-hump solitons in the dispersion decreasing fiber

Interaction properties of double-hump solitons in the dispersion decreasing fiber

Dispersive optical solitons along with integrability test and one soliton transformation for saturable cubic-quintic nonlinear media with nonlinear dispersion

Three well known properties of solitons will be discussed in this paper, like Painleve test (P-test), Hirota bilinear method (HBM) and extended modified auxiliary equation mapping (EMAEM) architectonic in saturable cubic quintic nonlinear media (SCQNM) in the presence of nonlinear dispersion. The P-test will be used to examine the integrability of our governing model. For finding multiple soliton interaction HBM scheme will be adopted. EMAEM architectonic will be implemented in order to obtain some new solitary wave solutions like bright dromion (soliton), domain wall, singular, periodic, doubly periodic, trigonometric, rational and hyperbolic solutions etc. Graphical outcomes (3D, 2D, and density plots) will be shown to reflect the actual behavior of results.

Parametric gap solitons in PT-symmetric optical structures

Abstract It is well known that quadratic nonlinearity and feedback through Bragg periodicity are the basis for parametric gap solitons. The major part of the relevant investigations refers to passive systems. At the same time, optical systems supplemented with active elements can demonstrate unusual properties. Asymmetry intrinsic to structures with parity-time (PT) symmetry is a bright confirmation of this statement. The interplay of nonlinearity, Bragg reflection and gain/loss profile can lead to the complicated pattern of wave interactions and novel results. In this study we address the properties of two-color solitons in complex PT symmetric periodic structures with quadratic nonlinearity. We focus on the case of single Bragg resonance. We reveal the region of parameters where stable parametric solitons may exist. We demonstrate that characteristics of forming solitons depend on the order of alteration of amplifying and absorbing layers.

Superfluid properties of bright solitons in a ring

We theoretically investigate superfluid properties of a one-dimensional annular superfluid with a boost. We derive the formula of the superfluid fraction in the one-dimensional superfluid, which was originally derived by Leggett in the context of supersolid. We see that the superfluid fraction given by Leggett's formula detects the emergence of solitons in the one-dimensional annular superfluid. The formation of a bright soliton at a critical interaction strength decreases the superfluid fraction. At a critical boost velocity, a node appears in the soliton and the superfluid fraction vanishes. With a transverse dimension, the soliton alters to a more localized one and it undergoes dynamical instability at a critical transverse length. Consequently, the superfluid fraction decreases as one increases the length up to the critical length. With a potential barrier along the ring, the uniform density alters to an inhomogeneous configuration and it develops a soliton localized at one of the potential minima by increasing the interaction strength.

Characteristic behavior and modulation instability of Peregrine solitons of the ion acoustic waves: a perspective of Titan’s ionosphere

The propagational properties of solitons along with peregrine solitonic modulational instability of ion acoustic (IA) waves are investigated taking into account the plasma properties of the Titan’s ionosphere. The Titan’s ionosphere typically consists of positive (, , and ) and negative (, , and ) ionic species along with electrons. In this study, it is assumed that the positive ions and electrons follow the Lorentzian-like kappa distribution. The fluid model equations are considered for negative ions. The Korteweg-de Vries (KdV) equation is derived using the reductive perturbation method to study the propagational properties and the characteristic behavior of solitons. In addition, the multiple-scale perturbation method is also used to derive the non-linear Schrödinger (NLS) equation for the analyses of modulational instability along with the production of rogue waves considering Peregrine solitonic solution. The dark solitons appear for the smaller wave numbers, whereas the bright solitons appear for the larger wave numbers. On the other hand, instability due to modulation is excited when the wave number is greater than its critical value, whereas it becomes stable when the wave number is smaller. The Peregrine soliton carries a single pick that decays to the plane wave asymptotic background either in space or time domain.

Hydrazone organics with third-order nonlinear optical effect for femtosecond pulse generation and control in the L-band

Dissipative solitons are generalized solitons with much larger pulse energy and width than conventional solitons, and the pulse characteristics will be changed dramatically during transmission. Nonlinear photonic absorption device in nonlinear optical resonator can provide saturable absorption effect to generate ultrashort pulses. However, most of the nonlinear photonics devices are based on inorganic materials such as two-dimensional materials with complex production process, and there are relatively few such researches on organics. In this paper, nonlinear photonics absorption device based on hydrazone organics with high molecular polarizability and significant third-order optical nonlinearity generate ultrashort pulses. The dissipative soliton pulses are obtained by controlling the dispersion, and the pulses are compressed to the near-transformation limit of 408 fs with a compression ratio of 44.6. More importantly, the extra-cavity transport properties of dissipative solitons are discussed. Dissipative noise-like soliton pulses are discovered after additional anomalous dispersion fiber, further demonstrating that the physical laws and optical properties of dissipative solitons are completely different from those of traditional optical pulses. We expect that these experimental advances can provide some experimental basis and support for the propagation of dissipative solitons.

Phase-matching-induced near-chirp-free solitons in normal-dispersion fiber lasers

Direct generation of chirp-free solitons without external compression in normal-dispersion fiber lasers is a long-term challenge in ultrafast optics. We demonstrate near-chirp-free solitons with distinct spectral sidebands in normal-dispersion hybrid-structure fiber lasers containing a few meters of polarization-maintaining fiber. The bandwidth and duration of the typical mode-locked pulse are 0.74 nm and 1.95 ps, respectively, giving the time-bandwidth product of 0.41 and confirming the near-chirp-free property. Numerical results and theoretical analyses fully reproduce and interpret the experimental observations, and show that the fiber birefringence, normal-dispersion, and nonlinear effect follow a phase-matching principle, enabling the formation of the near-chirp-free soliton. Specifically, the phase-matching effect confines the spectrum broadened by self-phase modulation and the saturable absorption effect slims the pulse stretched by normal dispersion. Such pulse is termed as birefringence-managed soliton because its two orthogonal-polarized components propagate in an unsymmetrical “X” manner inside the polarization-maintaining fiber, partially compensating the group delay difference induced by the chromatic dispersion and resulting in the self-consistent evolution. The property and formation mechanism of birefringence-managed soliton fundamentally differ from other types of pulses in mode-locked fiber lasers, which will open new research branches in laser physics, soliton mathematics, and their related applications.

Oscillation properties of matter-wave bright solitons in harmonic potentials

We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during their collisions. The modified oscillation periods are described by defining a characterized speed, with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases. The oscillation period can be used to distinguish the inter- and intra-species interactions between solitons. However, a bright soliton cannot oscillate in a harmonic trap, when it is coupled with a dark soliton (without any trapping potentials). Interestingly, it can oscillate in an anti-harmonic potential, and the oscillation behavior is explained by a quasi-particle theory. The modified period of two dark-bright solitons can be also described well by the characterized speed. These results address well the effects of position shift during soliton collision, which provides an important supplement for previous studies without considering phase shift effects.

Dynamics of matter-wave solitons in three-component Bose-Einstein condensates with time-modulated interactions and gain or loss effect

The gain or loss effect on the dynamics of the matter-wave solitons in three-component Bose–Einstein condensates with time-modulated interactions trapped in parabolic external potentials are investigated analytically. Some exact matter-wave soliton solutions to the three-coupled Gross–Pitaevskii equation describing the three-component Bose–Einstein condensates are constructed by similarity transformation. The dynamical properties of the matter-wave solitons are analyzed graphically, and the effects of the gain or loss parameter and the frequency of the external potentials on the matter-wave solitons are explored. It is shown that the gain coefficient makes the atom condensate to absorb energy from the background, while the loss coefficient brings about the collapse of the condensate.

Quasi-Yamabe solitons and almost quasi-Yamabe solitons on lightlike hypersurfaces

In the present paper, we study the quasi-Yamabe solitons and almost quasi-Yamabe solitons on the lightlike hypersurfaces of the semi-Riemannian manifolds endowed with a torse-forming vector field. We show some conditions for the lightlike hypersurfaces to be quasi-Yamabe solitons and almost quasi- Yamabe solitons with the tangential component of the torse-forming vector field on the semi-Riemannian manifolds as the soliton field. In particular, we also specify the conditions for lightlike hypersurfaces of (n + 2)-dimension semi-Riemannian manifolds of constant curvature to be quasi-Yamabe solitons and almost quasi-Yamabe solitons. Besides, we provide some geometric properties of the lightlike hypersurfaces satisfying quasi-Yamabe solitons, quasi-Yamabe gradient solitons, almost quasi-Yamabe solitons and almost quasi-Yamabe gradient solitons. Furthermore, we investigate properties of screen homothetic lightlike hypersurfaces admitting quasi-Yamabe solitons and almost quasi-Yamabe solitons.

Dynamics of two-dimensional multi-peak solitons based on the fractional Schrödinger equation

We address the propagation dynamics of two-dimensional multi-peak solitons in the optical lattices based on the fractional Schrödinger equation. The effect of Lévy index and lattice depth on the band-gap structure of optical lattices are presented. Two-, three-, four-, six- and eight-peak solitons all can exist in the first gap and be stable in a wide region of their existence domain. The effective width, maximal peak value and the power of soliton are also studied. It indicates that the Lévy index plays a significant role on the properties of solitons.

TANGENT BUNDLES ENDOWED WITH SEMI-SYMMETRIC NON-METRIC CONNECTION ON A RIEMANNIAN MANIFOLD

The differential geometry of the tangent bundle is an effective domain of differential geometry which reveals many new problems in the study of modern differential geometry. The generalization of connection on any manifold to its tangent bundle is an application of differential geometry. Recently a new type of semi-symmetric non-metric connection on a Riemannian manifold is studied and established a relationship between Levi-Civita connection and semi-symmetric non-metric connection. The various properties of a Riemannian manifold with relation to such connection are also discussed. The present paper aims to study the tangent bundle of a new type of semi-symmetric non-metric connection on a Riemannian manifold. The necessary and sufficient conditions for projectively invariant curvature tensors corresponding to such connection are proved and show many basic results on the Riemannian manifold in the tangent bundle. Furthermore, the properties of group manifolds of the Riemannian manifolds with respect to the semi-symmetric non-metric connection in the tangent bundle are studied. Moreover, theorems on the symmetry property of Ricci tensor and Ricci soliton in the tangent bundle are established.

Boomerons in a three-coupled NLS system with inhomogeneous dispersion and nonlinearity

This study investigates the dynamics of boomerang solitons and their interactions in three-mode fiber under the influence of inhomogeneous effects governed by three-coupled nonlinear Schrödinger (3-CNLS) equations in GVD and nonlinearity coefficients. Also, 3-CNLS equation can be used to investigate the optical soliton propagation in three-core fibers, which contain some potential applications in the optical fiber communication system. Using the Darboux transformation method with computer simulation, the two-bright boomerang soliton solutions are attained analytically for the dispersion and nonlinearity functions. The propagation and interaction properties of boomerang solitons are investigated, while the variable coefficients are adopted as linear functions. Various interaction scenarios are illustrated by plotted figures to reveal the importance of obtained soliton solutions. The physical significance of boomerang solitons can be understood from the displayed figures. The obtained results will be benefit soliton path control and soliton phase management in an inhomogeneous three-core optical fiber.

Valley Hall edge solitons in a photonic graphene.

We predict the existence and study properties of the valley Hall edge solitons in a composite photonic graphene with a domain wall between two honeycomb lattices with broken inversion symmetry. Inversion symmetry in our system is broken due to detuning introduced into constituent sublattices of the honeycomb structure. We show that nonlinear valley Hall edge states with sufficiently high amplitude bifurcating from the linear valley Hall edge state supported by the domain wall, can split into sets of bright spots due to development of the modulational instability, and that such an instability is a precursor for the formation of topological bright valley Hall edge solitons localized due to nonlinear self-action and travelling along the domain wall over large distances. Topological protection of the valley Hall edge solitons is demonstrated by modeling their passage through sharp corners of the Ω-shaped domain wall.

Confinement of bright matter-wave solitons on top of a pedestal-shaped potential

Reflection of wave packets from downward potential steps and attractive potentials, known as a quantum reflection, has been explored for bright matter-wave solitons and breathers with the main emphasis on the possibility to trap them on top of a pedestal-shaped potential. In numerical simulations with particular parameter settings, we observed that moving solitons return from the borders of the potential and remain trapped for a sufficiently long time. The shuttle motion of the soliton is accompanied by shedding some amount of matter at each reflection from the borders of the trap, thus reducing its norm. The time-shift observed in a step-like decay of the moving soliton's norm in the two-soliton configuration is linked to the trajectory jump phenomenon. In the framework of the proposed model, several fundamental properties of solitons have been illustrated, such as a discontinuous jump of trajectories of colliding solitons, splitting of the breather, and the absence of matter exchange between interacting solitons. The obtained results can be of interest for the design of new soliton experiments with Bose-Einstein condensates.