Exotic Solitons Research Articles

Editorial: Nucleation and stability of exotic solitons in condensed matter

Editorial: Nucleation and stability of exotic solitons in condensed matter

Chaotic behaviors, exotic solitons and exact solutions of a nonlinear Schrödinger-type equation

In this paper, qualitative analysis is used to study a nonlinear Schrödinger-type equation. By applying traveling wave transform and choosing different parameter values, we obtain two types of dynamic systems. We apply the qualitative method to show that there are periodic solutions, optical solitary waves and exotic solitons for the equation. Then we perform the quantitative analysis to these different dynamic systems and obtain the corresponding exact solutions, which verifies the correctness of our previous conclusions. In addition, some new solutions are also constructed, such as, rational solutions and double period elliptic function solution. Finally, we add different perturbed forms to the dynamic system and obtain the largest Lyapunov exponents and corresponding phase diagrams, which demonstrates the existence of chaotic behaviors of the equation. To the best of our knowledge, the chaotic behaviors of the equation we obtained are firstly proposed.

2-D exotic soliton in 2-D Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction

2-D exotic soliton in 2-D Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction

2-D exotic soliton in 2-D Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction

The two-dimensional (2D) version of ferromagnet XXZ spin chain with DzyaloshinskyMoriya (DM) interaction, recently introduced by F. Kenmogne and coworkers is reexplored. Firstly by using the Dyson-Maleev transformation, the 2-D discrete nonlinear Schrödinger (DNLS) equation, governing the quantum states behaviors is found. Next using the semidiscrete multiple-scale method, the 2-D DNLS equation is reduced to the 2D extended nonlinear Schrödinger (ENLS) equation which consists of the basic 2-D NLS equation with additional nonlinear dispersive terms. This equation admits the classical 2D pulse quantum states, when additional terms vanish. In addition, this equation admits the 2D compacton and 2D peakon-like boson quantum states. Furthermore, we notice that on the contrary to the classical outcomes where amplitudes of both solutions are free parameters, the amplitudes for two dimensional quantum states are not free parameters since the obtained solutions need to be normalized.

M-shaped and other exotic solitons generated by cubic-quintic saturable nonlinearities in a nonlinear electrical transmission network with higher-order dispersion effects

This investigation presents the generalized cubic-quintic Guizburg-Landau (GCQGL) equation with higher-order dispersion effects in a nonlinear electrical transmission network. Based on the collective coordinates' theory with a conventional Gaussian Ansatz, the study reveals that the waves which propagate in this medium are exotic solitons such as M-shaped solitons. The investigation presents the stability of the dark soliton subjected to the quintic-phase modulation. Besides, the introduction of the cubic- and quintic-saturable nonlinearities induce the generation of twin narrow solitons, M-shaped soliton and Sasa-Satsuma soliton. Moreover, the introduction of the third-order dispersion (TOD) and the fourth-order dispersion (FOD) provokes the generation of twin large solitons associated to symmetric radiation lobes and twin narrow solitons associated to the damping effect. Some exact field solutions of the GCQGL equation are also illustrated. Moreover, some theoretical frequencies are found where significant results are exposed. In addition, physical conditions associated to the saturation lead to a particular internal perturbation. This internal excitation is measured in detail by the collective coordinates in order to build-up exotic solitons. This technique improves the comprehension of some exotic waves' mechanism of generation in nonlinear electrical transmission network.

Dynamics of dissipative soliton molecules in a dual-wavelength ultrafast fiber laser.

Optical solitons, particle-like excitations ubiquitous in many fields, can bind to form soliton molecules with striking molecule-like interactions. However, the exotic soliton interactions in soliton molecules are still largely unexplored in dual-wavelength mode-locked fiber lasers. Here, we reveal the dynamics of dissipative soliton molecules with periodic solitons collision in a dual-wavelength ultrafast fiber laser. The soliton molecules with a central wavelength of 1532.8 nm and 1561 nm exhibit conspicuously different evolution characteristics attributed to the difference in gain spectral intensity and trapped potential. The long-wavelength soliton molecule swiftly recovers to the initial state after collision, while the short-wavelength soliton molecule has a remarkable variation in temporal separation and operation state. Moreover, the multiple intensive repulsion and attraction in soliton molecule with energy transfer between leading and trailing solitons, and the formation of triplet soliton molecule in short-wavelength with multiple switching have also been observed. The different oscillating solutions coexisting in dual-wavelength soliton molecules involving oscillating and sliding phase evolution confirm the multistability of the dissipative system. These findings shed new insights into the dynamics of soliton molecules and solitons collision in nonlinear systems.

W-shaped and other solitons in optical nanofibers

The main objective of this study is to investigate W-shaped and other types of optical solitons in nano optical fibers. The medium is described by perturbed nonlinear Schrödinger equation with Kerr law nonlinearity. The study is carried out by means of three exotic soliton ansatzes. Consequently, different forms of W-shaped solitons are derived under specific conditions. It is found that the formation of W-shaped solitons depends on the balance between the self-steepening effect and the nonlinear dispersion. Due to some restrictions, W-shaped solitons experience a decay into bright or dark solitons. Besides, numerous types of soliton solutions that describe different structures of optical solitons are extracted. These structures include bright, dark, kink-dark, kink and anti-kink solitons. The existence conditions of all optical solitons are presented. The behaviours of optical solitons are illustrated graphically by selecting suitable values for the physical parameters.

Soliton collision induced explosions in a mode-locked fibre laser

Soliton explosion refers to a striking nonlinear dynamics in dissipative systems. In this state, a dissipative soliton collapses but returns back to its original state afterwards. Yet, the origin of such exotic soliton dynamics remains elusive. Here it is revealed that soliton collision can induce soliton explosions in a mode-locked fibre laser, benefiting from synchronous measurements of the spatio-temporal intensity evolution and the real-time spectra evolution using dispersive Fourier transform. Up to seven nonlinear regimes are observed successively in the laser by increasing the pump power only, including single-pulse mode locking, standard soliton explosions, noise-like mode locking, stable double pulsing, soliton collision induced explosions, soliton molecules, and double-pulse noise-like mode locking. These experimental findings are conducive to understand complex soliton dynamics in many nonlinear dissipative systems.

Tuning the Dipole-Dipole Interaction in a Quantum Gas with a Rotating Magnetic Field.

We demonstrate the tuning of the magnetic dipole-dipole interaction (DDI) within a dysprosium Bose-Einstein condensate by rapidly rotating the orientation of the atomic dipoles. The tunability of the dipolar mean-field energy manifests as a modified gas aspect ratio after time-of-flight expansion. We demonstrate that both the magnitude and the sign of the DDI can be tuned using this technique. In particular, we show that a magic rotation angle exists at which the mean-field DDI can be eliminated, and at this angle, we observe that the expansion dynamics of the condensate is close to that predicted for a nondipolar gas. The ability to tune the strength of the DDI opens new avenues toward the creation of exotic soliton and vortex states as well as unusual quantum lattice phases and Weyl superfluids.

The dynamics of aloof baby Skyrmions

The aloof baby Skyrme model is a (2+1)-dimensional theory with solitons that are lightly bound. It is a low-dimensional analogue of a similar Skyrme model in (3+1)-dimensions, where the lightly bound solitons have binding energies comparable to nuclei. A previous study of static solitons in the aloof baby Skyrme model revealed that multi-soliton bound states have a cluster structure, with constituents that preserve their individual identities due to the short-range repulsion and long-range attraction between solitons. Furthermore, there are many different local energy minima that are all well-described by a simple binary species particle model. In this paper we present the first results on soliton dynamics in the aloof baby Skyrme model. Numerical field theory simulations reveal that the lightly bound cluster structure results in a variety of exotic soliton scattering events that are novel in comparison to standard Skyrmion scattering. A dynamical version of the binary species point particle model is shown to provide a good qualitative description of the dynamics.

Bright and exotic solitons in optical metamaterials by semi-inverse variational principle

This paper addresses solitons in optical metamaterials. The semi-inverse variational principle (SVP) is utilized to secure bright soliton solutions to the governing model. There are five forms of nonlinearity that are studied in this paper. They are Kerr law, power law, parabolic law, dual-power law and finally the log law nonlinearity. In particular for Kerr law nonlinearity, there are two additional forms of soliton solutions obtained. They are cosh-Gaussian pulses and bright-dark combo solitons and these are collectively being referred to as exotic solitons. There are several constraint conditions that naturally emerge for these solitons to exist.

A sine-Gordon cellular automaton and its exotic solitons

We study the solitons of the ultradiscrete potential sine-Gordon equation and their interaction. We show that the collision of these solitons can be either elastic or inelastic. In the latter case, a soliton can emerge from the interaction either longer (dressed) or shorter (undressed), but there are upper and lower limits on the possible lengths of each soliton. Starting from the relation of the discrete sine-Gordon to the discrete KdV, we derive its ultradiscrete analogue and use it to transpose the study of the interaction of the sine-Gordon solitons to the dynamics of the solutions of KdV. The latter is represented by symbolic-like dynamics of the background term present in the ultradiscrete KdV equation. We introduce a new elementary entity, dubbed ‘oiston’, and describe these dynamics as the interaction of the latter. This allows us to explain the dressing and undressing of the sine-Gordon solitons as well as the fact that this process has a fixed capacity for every soliton.

Ferroelectricity in synthetic metals: Reality and hypotheses

Ferroelectricity is one of the demanded effects in fundamental and applied solid state physics. Till now, the ferroelectrics were available mostly in the inorganic world. The breakthrough of 2000s was an unexpected discovery of the ferroelectricity related to the charge ordering in quasi-1D organic conductors (TMTTF) 2X, and in some layered compounds. The achieved understanding of underlying mechanisms allows to speculate on synthesis of a would-be ferroelectric polymer: it must possess a combination of dimerizations of sites and bonds, one of which must be build-in and another spontaneous. The theory of these “combined Peierls states” predicts an existence of solitons (dimerization kinks) with non-integer variable charges—they are the walls separating domains with opposite electric polarization. The physics of these exotic solitons will serve to describe transient processes in ferroelectric polymers, linking optical- and low-frequency properties. The promising example of such an (AB) x conjugated polymer has already appeared but was not yet tested for ferroelectricity. A wide chemical search is necessary because of a problematic competition of an anti-ferroelectric phase, whose occurrence depends on complicated details of the interchain coupling.

Nonlocal and nonlinear dispersion in a nonlinear Schrödinger-type equation: exotic solitons and short-wavelength instabilities

We study the continuum limit of a nonlinear Schrödinger lattice model with both on-site and inter-site nonlinearities, describing weakly coupled optical waveguides or Bose–Einstein condensates. The resulting continuum nonlinear Schrödinger-type equation includes both nonlocal and nonlinear dispersion. Looking for stationary solutions, the equation is reduced to an ordinary differential equation with a rescaled spectral parameter and a single parameter interpolating between the nonlocality and the nonlinear dispersion. It is seen that these two effects give a similar behaviour for the solutions. We find smooth solitons and, beyond a critical value of the spectral parameter, also nonanalytic solitons in the form of peakons and capons. The existence of the exotic solitons is connected to the special properties of the phase space of the equation. Stability is investigated numerically by calculating eigenvalues and eigenfunctions of the linearized problem, and we particularly find that with both nonlocal and nonlinear dispersion simultaneously present, all solutions are unstable with respect to a break-up into short-wavelength oscillations.

Solitons in elastic plates

The nonlinear dynamics of elastic shear waves is investigated taking into account the interaction of the shear component of the displacements with low-amplitude sagittal components. Nonlinear evolutionary equations are derived for the shear-displacement field. These equations contain additional nonlinear dispersion terms due to the interaction with displacements in the sagittal plane. The soliton solutions of the equations obtained are studied and the possibility of the existence of exotic solitons—compactons and peakons—is discussed.

Exotic solitons in magnets with strongly anisotropic exchange interaction

Exotic magnetic solitons (compactons and peakons) in magnets with extremely anisotropic exchange interaction are investigated on the basis of the classical Ising and XY-models.

Bose gas with nontrivial particle interaction and semiclassical interpretation of exotic solitons

Many-particle bound states in a Bose gas with a complex pair interaction between particles are considered. It is shown that the combination of attraction and repulsion between particles leads to the emergence of bound states with peculiar physical properties. In the limit of a large number of bound states in the Hartree approximation, these states are close in the structure and properties to exotic solitons (compactons and peakons) in classical systems with weak spatial dispersion. Examples of exotic solitons of various types in magnetically ordered media are considered.

Effects of Impurities in Polyacetylene –Site-Type Short-Ranged Impurities–

Effects of short ranged bond-type impurities in polyacetylene are investigated numerically, using a generalized Su-Schrieffer-Heeger's model. Soliton formation and pinning by impurities are studied. Infrared activities are analyzed with relevant phonons. Similarities and differences from site-type impurities are pointed out. It is striking to find that there may be two types of exotic “solitons”. One is a kink in the bond alternation configuration which carries neither charge nor spin. The other is a soliton with a fractional charge and a fractional spin, which appears in a situation where the polaron solution is stable in the absence of impurities. The stabilization of the exotic solitons is associated with the fact that the particle-hole symmetry still holds in the presence of the bond-type impurities.

Backlund transformation for equations which exhibit exotic soliton solutions

Backlund transformation for equations which exhibit exotic soliton solutions

The Bäcklund transformations for nonlinear evolution equations which exhibit exotic solitons

By an analysis of the normalization condition of the Hilbert-Riemann problem associated to the spectral problem of the Wadati-Konno-Ichikawa equation we are able to get a deeper view on the Bäcklund transformation for this system. The results obtained are extended to the Harry-Dym equation and to a whole set of nonlinear evolution equations which exhibit exotic solitons. In the end we are able to find out new nonlinear evolution equations which share these properties.