Soliton Phase Research Articles

Solitary waves and stable analysis for the quintic discrete nonlinear Schrödinger equation

The quintic discrete nonlinear Schrödinger equation (QDNLS) is an important model for describing the propagation of discrete self-trapped beams in an array of weakly coupled nonlinear optical waveguides. In this paper, the QDNLS is studied and bright solitons, dark solitons, alternating phase solitons, trigonometric function periodic wave solutions and rational wave solutions with arbitrary parameters are obtained using the extended G'/G-expansion method. The linear stability of the bright soliton, the dark soliton and the rational wave solution is analyzed using the perturbation method, and the conditions that stable solitary wave solutions satisfy are presented. The stable solitary wave solutions to the QDNLS are useful in understanding the complicated physical phenomena described by QDNLS.

Phase solitons in multi-band superconductors with and without time-reversal symmetry

The Josephson-like interband couplings in multi-band superconductivity exhibit degenerate energy minima, which support states with kinks in phase of superconductivity. When the interband couplings in systems of three or more components are frustrated, the time-reversal symmetry (TRS) can be broken, which generates another type of phase kink between the two time-reversal symmetry breaking (TRSB) pair states. In this work, we focus on these novel states of phase kinks, and investigate their stability, similarity, differences and physical consequences. The main results can be summarized as follows: (i) we find a new type of phase slip when the kink becomes unstable. (ii) In the kink region, TRS is broken and spontaneous magnetic fields are induced. (iii) In superconductors with TRSB, composite topological excitations associated with variations of both the superconductivity phase and amplitude can be created by local perturbations or due to proximity effect between normal metals.

Nonautonomous Solitons in the (3+1)-Dimensional Inhomogeneous Cubic-Quintic Nonlinear Medium

We have constructed explicit nonautonomous soliton solutions of the generalized nonlinear Schrödinger equation in the (3+1)-dimensional inhomogeneous cubic-quintic nonlinear medium. The gain parameter has no effects on the motion of the soliton's phase or their velocities, and it affects just the evolution of their peaks. As two examples, we discuss the propagation of nonautonomous solitons in the periodic distributed amplification system and the exponential dispersion decreasing system. Results show that the presence of the chirp not only makes the intensity of solitons weaken more promptly, but also broadens their width.

Dynamics of solitons in a nonintegrable version of the modified Korteweg-de Vries equation

Nonlinear wave dynamics is discussed using the extended modified Korteweg-de Vries equation that includes the combination of the third- and fifth-order terms and is valid for waves in a three-layer fluid with so-called symmetric stratification. The derived equation has solutions in the form of solitary waves of various polarities. At small amplitudes, they are close to solitons of the modified Korteweg-de Vries equation. However, the height of large-amplitude solutions has a limit approaching which solitary waves widen and acquire a table like shape similar to soluitons of the Gardner equation. Numerical calculations confirm that the collision of solitons of the derived equation is inelastic. Inelasticity is the most pronounced in the interaction of unipolar pulses. The direction of the shift of the phase of the higher-amplitude soliton owing to the interaction of solitons of different polarities depends on the amplitudes of the pulses.

Evolution of the spin-density wave-superconductivity texture in the organic superconductor (TMTSF)2PF6 under pressure

We report an investigation at the endpoint region of the spin density wave state in (TMTSF)2PF6 where metal and superconductivity emerge. Thanks to resistivity measurements along the three main crystallographic directions, we are able to follow the texture in this phase coexistence regime. In this respect, superconductivity is used as a decoration technique of the metallic pattern. We show that metal (superconductivity) emerges first along the c⁎ direction in a counterintuitive manner. Then metal (superconductivity) domains evolves from filaments along the c⁎ axis towards slabs perpendicular to the a-axis which melt together in the homogeneous phase at high pressure. This evolution is compatible with the proposition of the formation of a soliton phase in the vicinity of the critical pressure of the (TMTSF)2PF6 phase diagram.

Charged nontopological soliton of the SU(2) × U(1) gauge model

The SU(2) × U(1) gauge model that is the bosonic sector of the Standard Model of electroweak interactions is considered. The existence of electrically charged nontopological solitons is shown to be possible in this model. Some properties of a charged nontopological soliton are investigated. Asymptotic expressions are derived for the soliton radius, energy, and phase frequency in the thin-wall regime by the method of trial functions. Numerical solutions of the model field equations corresponding to electrically charged non-topological solitions have been obtained. The dependences of the soliton energy and charge on phase frequency are given for several model parameters. It follows from the data obtained that there exists a domain of parameters in which a charged nontopological soliton is stable to the transition to a plane-wave field configuration.

Multi-Soliton Solutions for an Inhomogeneous Nonlinear Schrödinger– Maxwell–Bloch System in the Erbium-Doped Fiber

Under investigation in this paper is an inhomogeneous nonlinear Schrödinger-Maxwell-Bloch system with variable dispersion and nonlinear effects, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber. Under certain coefficient constraints, multi-soliton solutions are obtained by the Hirota method and symbolic computation. Evolution and interaction of the solitons are plotted, and the self-induced transparency effect caused by the doped erbium atoms is found to lead to the change of the soliton velocity and phase. Overall phase shift can be observed when the parameter accounting for the interaction between the silica and doped erbium atoms is taken as a constant.

Tunable oscillation of discrete solitons triggered by coherent interactions

We report on a tunable oscillation behavior of discrete solitons triggered by coherentsoliton interactions in optically induced photonic lattices. Such oscillation originates fromthe interplay between the soliton transverse motion caused by soliton interaction and theBragg reflection of the lattice structures. We show that such oscillations can becontrolled either by the lattice beam intensity or the amplitude of the externalbias field. Selective triggers of the oscillation for the desirable soliton are alsoobtained by tuning the input soliton power and/or the soliton phase differences.

Observing Majorana bound states of Josephson vortices in topological superconductors

In recent years there has been an intensive search for Majorana fermion states in condensed matter systems. Predicted to be localized on cores of vortices in certain nonconventional superconductors, their presence is known to render the exchange statistics of bulk vortices non-abelian. Here we study the equations governing the dynamics of phase solitons (fluxons) in a Josephson junction in a topological superconductor. We show that the fluxon will bind a localized zero energy Majorana mode and will consequently behave as a non-abelian anyon. The low mass of the fluxon, as well as its experimentally observed quantum mechanical wave-like nature, will make it a suitable candidate for vortex interferometry experiments demonstrating non-abelian statistics. We suggest two experiments that may reveal the presence of the zero mode carried by the fluxon. Specific experimental realizations will be discussed as well.

Characteristics of Internal Waves in the South China Sea Observed by a Shipboard Coherent Radar

In 2005 and 2007, a coherent X-band radar was deployed in the South China Sea on two different ships. In both cases, the two parabolic antennas of the radar were fixed at grazing angles of approximately 2° looking toward the bow of the ship. The radar transmitted and received through a single antenna but alternated between the two antennas approximately every half second. One antenna was horizontally polarized and the other was vertically polarized. The data were analyzed by computing normalized radar cross sections and scatterer velocities as a function of ground range and time. Surface signatures of internal waves were obvious in both types of image and at both polarizations as regions of enhanced cross sections or scatterer velocities. The collected imagery showed that at least two different types of internal waves exist in the South China Sea: small, nearly sinusoidal trains of waves and large soliton-like waves. These different types traveled at very different speeds and interacted with each other. The small nearly sinusoidal waves traveled at phase speeds near 1 m/s that appeared to increase as the small wave trains were overtaken by the faster solitons. Combined with other shipboard measurements, the radar measurements yielded the widths, maximum velocities, and strain rates of the solitons as well as the dependence of phase speed on amplitude. When the speeds of both the ship and the solitons were removed, the measurements showed that soliton full-widths at half-maximum ranged from about 0.5-4.5 km. These widths showed a dependence on the amplitude of the soliton. The phase speeds of the solitons also depended on their amplitude, reaching 3 m/s in deep water but only about 1.2 m/s in shallow water. CTD profiles were used to estimate an interface depth for a two-layer fluid model of the propagation of the solitons. The phase speeds predicted by this model agreed well with the observed dependence of the soliton phase speed on amplitude in both shallow and deep water.

Noise bandwidth dependence of soliton phase in simulations of stochastic nonlinear Schrödinger equations

We demonstrate that soliton perturbation theory, though widely used, predicts an incorrect phase distribution for solitons of stochastically driven nonlinear Schrödinger equations in physically relevant parameter regimes. We propose a simple variational model that accounts for the effect of radiation on phase evolution and correctly predicts its distribution.

Storage by trapping and spatial staggering of multiple interacting solitons inΛ-type media

In this paper we investigate the properties of self induced transparency (SIT) solitons, propagating in a $\Lambda$-type medium. It was found that the interaction between SIT solitons can lead to trapping with their phase preserved in the ground state coherence of the medium. These phases can be altered in a systematic way by the application of appropriate light fields, such as additional SIT solitons. Furthermore, multiple independent SIT solitons can be made to propagate as bi-solitons through their mutual interaction with a separate light field. Finally, we demonstrate that control of the SIT soliton phase can be used to implement an optical exclusive-or gate.

Phase Engineering and Solitons of Bose–Einstein Condensates with Two- and Three-Body Interactions

We introduce a phase imprint into the macroscopic order parameter governing the dynamics of Bose–Einstein condensates with attractive two-body interactions described by a cubic Gross–Pitaevskii (GP) equation and then engineer the imprinted phase suitably to generate the modified GP equation. The modified GP equation describes the dynamics of condensates with both two- (attractive) and three-body (attractive and repulsive) interactions in an expulsive harmonic trap. Employing gauge transformation approach, we then construct bright solitons of the modified GP equation. We observe that the attractive three-body interactions introduce an additional nontrivial phase in the matter wave solitons arising due to attractive two-body interactions without changing their density while the repulsive three-body interactions enormously increase the density of the condensates without causing any change in the phase of the solitons originating from attractive two-body interactions.

Gray photorefractive polymeric optical spatial solitons

We show that gray spatial optical solitons are possible in biased photorefractive polymers under steady-state conditions. We find that for a given material parameter the absolute value of a gray photorefractive polymeric soliton's phase decreases with an increase in the beam's grayness, whereas it increases with the material parameter for a given beam's grayness and that the full width half maximum (FWHM) of the gray soliton beam's intensity increases with the beam's grayness when the normalized background intensity and the material parameter are fixed and decreases with an increase in the normalized background intensity when the material parameter is fixed. On the other hand, we also show that N coupled beam evolution equations in biased photorefractive polymers can exhibit multicomponent gray solitons. These multicomponent gray solitons can be obtained provided that the N coupled beams share the same polarization, wavelength, and are incoherent with one another. The characteristics and stability properties of these multicomponent gray solitons are also discussed in detail.

Polymorphism of condensed phase of dissipative solitons

A two-component model of the reaction-diffusion type that was previously proposed for the interpretation of self-organization of current structures in semiconductor- discharge gap systems (including the description of dissipative solitons) is considered. The results of numerical simulations demonstrate the possible polymorphism of crystalline dissipative structures consisting of dissipative solitons.

Interplay Between Dispersion and Nonlinearity in Femtosecond Soliton Management

In this paper, we investigate the inhomogeneous higher-order nonlinear Schr¨odinger (NLS) equation governing the femtosecond optical pulse propagation in inhomogeneous fibers using gauge transformation and generate bright soliton solutions from the associated linear eigenvalue problem. We observe that the amplitude of the bright solitons depends on the group velocity dispersion (GVD) and the self-phase modulation (SPM) while its velocity is dictated by the third-order dispersion (TOD) and GVD. We have shown how the interplay between GVD, SPM, and TOD can be profitably exploited to change soliton width, amplitude (intensity), shape, phase, velocity, and energy for an effective femtosecond soliton management. The highlight of our paper is the identification of ‘optical similaritons’ arising by virtue of higher-order effects in the femtosecond regime.

Soliton rains in a fiber laser: An experimental study

Rains of solitons constitute a class of nonlinear dynamics of dissipative soliton ensembles that we briefly reported in Opt. Express 17, 11776 (2009) from a fiber laser experiment. The existence of a relatively intense noisy background together with several tens of soliton pulses aggregated in a condensed soliton phase constitutes a necessary condition for their appearance. New soliton pulses form spontaneously from the background fluctuations and drift until they reach the condensed soliton phase. We here relate in detail the experimental conditions under which soliton rains manifest and their key features, describe related dynamics observed in their vicinity, and propose an explanation for soliton rain dynamics.

Stability and dynamics of two-soliton molecules

The problem of soliton-soliton force is revisited. From the exact two-soliton solution of a nonautonomous Gross-Pitaevskii equation, we derive a generalized formula for the mutual force between two solitons. The force is given for arbitrary soliton amplitude difference, relative speed, phase, and separation. The latter allows for the investigation of soliton molecule formation, dynamics, and stability. We reveal the role of the time-dependent relative phase between the solitons in binding them in a soliton molecule. We derive its equilibrium bond length, spring constant, frequency, effective mass, and binding energy of the molecule. We investigate the molecule's stability against perturbations such as reflection from surfaces, scattering by barriers, and collisions with other solitons.

Domain walls at the spin-density-wave endpoint of the organic superconductor(TMTSF)2PF6under pressure

We report a comprehensive investigation of the organic superconductor ${(\text{TMTSF})}_{2}{\text{PF}}_{6}$ in the vicinity of the endpoint of the spin-density-wave metal phase transition where phase coexistence occurs. At low temperature, the transition of metallic domains toward superconductivity is used to reveal the various textures. In particular, we demonstrate experimentally the existence of one-dimensional and two-dimensional (2D) metallic domains with a crossover from a filamentary superconductivity mostly along the ${c}^{\ensuremath{\star}}$ axis to a 2D superconductivity in the ${b}^{\ensuremath{'}}c$-plane perpendicular to the most conducting direction. The formation of these domain walls may be related to the proposal of a soliton phase in the vicinity of the critical pressure of the ${(\text{TMTSF})}_{2}{\text{PF}}_{6}$ phase diagram.

Quantum transport in ladder-type networks: the role of nonlinearity, topology and spin

We investigate the quantum transport of electrons, phase solitons, etc, through the mesoscopic networks of zero-dimensional quantum dots. Straight and circular ladders are chosen as networks with each coupled with three semi-infinite leads (with one incoming and the other two outgoing). Two transmission probabilities as functions of the incident energy ε show a transition from anti-phase aperiodic to degenerate periodic spectra at the critical energy εc which is determined by a bifurcation point of the bulk energy dispersions. TPs of the circular ladder depend only on the parity of the winding number. The introduction of a single missing bond (MB) or missing step doubles the period of the periodic spectra at ε > εc. Shift of the MB by a lattice constant results in a striking switching effect at ε < εc. In the presence of the electric-field-induced spin–orbit interaction (SOI), an obvious spin filtering occurs for the spin-unpolarized injection. For the spin-polarized injection, on the other hand, the spin transport shows spin-flip (magnetization reversal) oscillations with respect to SOI. We also show a role of soliton in the context of its transport through the ladder networks.