Photon-Solitons and Some Experimental Possibilities

In this paper we show that the possible existence of the photon as a soliton [1] can be studied with the help of well-known experimental results and we propose some new experiments which can help to examine some properties of the soliton. First, we compare the soliton energy density to the energy density of Planck and we show that the two densities are consistent. Second, we make an attempt to explain some old experiments with our soliton model of the photon and we show that the results of such experiments do not contradict the existence of such solitons. We also discuss the possibilities for new, improved experiments, which can help to distinguish the soliton interaction from the interaction of a classical electromagnetic wave with charged particles.     

Solitonic fullerene structures in light atomic nuclei

The Skyrme model is a classical field theory which has topological soliton solutions. These solitons are candidates for describing nuclei, with an identification between the numbers of solitons and nucleons. We have computed numerically, using two different minimization algorithms, minimum energy configurations for up to 22 solitons. We find, remarkably, that the solutions for seven or more solitons have nucleon density isosurfaces in the form of polyhedra made of hexagons and pentagons. Precisely these structures arise, though at the much larger molecular scale, in the chemistry of carbon shells, where they are known as fullerenes.     

Nonlinear chiral models: Soliton solutions and spatio-temporal chaos

Nonlinear effective Lagrangian models with a chiral symmetry have been used to describe strong interactions at low energy, for a long time. The Skyrme model and the chiral quark-meson model are two such models, which have soliton solutions which can be identified with the baryons. We describe the various kinds of soliton states in these nonlinear models and discuss their physical significance and uses in this review. We also study these models from the view point of classical nonlinar dynamical systems. We consider fluctuations around theB=1 soliton solutions of these models (B, being the baryon number) and solve the spherically symmetric, time-dependent systems. Numerical studies indicate that the phase space around the Skyrme soliton solution exhibits spatio-temporal chaos. It is remarkable that topological solitons signifying stability/order and spatio-temporal chaos coexist in this model. In contrast with this, the soliton of the quark-meson model is stable even for large perturbations.     

Families of Bragg-grating solitons in a cubic–quintic medium

We investigate the existence and stability of solitons in an optical waveguide equipped with a Bragg grating (BG) in which nonlinearity contains both cubic and quintic terms. The model has straightforward realizations in both temporal and spatial domains, the latter being most realistic. Two different families of zero-velocity solitons, which are separated by a border at which solitons do not exist, are found in an exact analytical form. One family may be regarded as a generalization of the usual BG solitons supported by the cubic nonlinearity, while the other family, dominated by the quintic nonlinearity, includes novel “two-tier” solitons with a sharp (but nonsingular) peak. These soliton families also differ in the parities of their real and imaginary parts. A stability region is identified within each family by means of direct numerical simulations. The addition of the quintic term to the model makes the solitons very robust: simulating evolution of a strongly deformed pulse, we find that a larger part of its energy is retained in the process of its evolution into a soliton shape, only a small share of the energy being lost into radiation, which is opposite to what occurs in the usual BG model with cubic nonlinearity.     

Superposition solitons in two-component Bose-Einstein condensates

We develop the Hirota bilinear method and obtain the exact one and two superposition soliton solutions for two-component Bose-Einstein condensates. The conversion of three kinds of solitons including the superposition solitons, bright-bright solitons, and dark-bright solitons is discussed. With the energy analysis, we find that the superposition soliton state is an excitation state for this system. Moreover, the collision of two superposition solitons is found to be elastic.     

Propagation characteristics of parallel dark solitons in silicon-on-insulator waveguide

The propagation characteristic of two identical and parallel dark solitons in a silicon-on-insulator(SOI) waveguide is simulated numerically using the split-step Fourier method. The parallel dark solitons imposed by the initial chirp are investigated mainly by changing their power, their relative time delay. The simulation shows that the time delay deforms the parallel dark soliton pulse, forming a bright-like soliton in the transmission process and making the transmission quality down. By increasing the power of one dark soliton, the energy of the other dark soliton can be increased, and larger increase in a soliton's power leads to larger increase in the energy of the other. When the initial chirp is introduced into one of the dark solitons, higher energy consumption is observed. In particular, positive chirps resulting in pulse broadening width while negative chirps narrowing, with an obvious compression effect on the other dark soliton. Finally, large negative chirps are found to have a profound impact on parallel and nonparallel dark solitons.     

Waveguides induced by steady-state gray solitons in biased photorefractive-photovoltaic crystals

We carry out a theoretical investigation of the properties of waveguides induced by photorefractive one-dimensional steady-state gray spatial solitons (i.e., screening solitons, photovoltaic solitons, and screening-photovoltaic solitons). We demonstrate that waveguides induced by photorefractive steady-state gray spatial solitons are only a single guided mode for both all soliton graynesses and all values of ρ, where ρ is the ratio between the soliton peak intensity and the dark irradiance, and moreover, waveguides induced by gray photovoltaic solitons for closed-circuit condition are also only a single guided mode for all electric current densities. We find that the confined energy near the center of a photorefractive steady-state gray spatial soliton increases with ρ and decreases with an increase in the soliton grayness. We also find that the confined energy near the center of a gray photovoltaic soliton for closed-circuit condition increases with the electric current density. On the other hand, waveguides induced by gray screening-photovoltaic solitons are gray screening soliton-induced waveguides when the bulk photovoltaic effect is neglectable and are gray photovoltaic soliton-induced waveguides when the external bias field is absent.     

Nucleons in nuclei in the selfconsistent soliton model to QCD

In the scalar Soliton model of QCD the gluon field operators are replaced by a classical selfcoupling scalar field with solitontype interaction. The quark wave-functions and the soliton field are calculated for the free nucleon as compared to a nucleon inside nuclear matter approximated by averaged boundary conditions to simulate the surrounding nucleons. The mass of the nucleon as well as its mean effective radius are given in terms of the nuclear-matter density and the model parameters. For large quark-soliton coupling the EMC-effect is seen, and then at high densities a plasma of free quarks and free localized solitons is the lowest energy solution.     

Splitting of strain solitons upon their interaction

The results from analytical studies and numerical simulations of strain soliton interaction are presented. It is shown that soliton collisions are of an inelastic character; i.e., secondary (daughter) solitons with lower energies are produced after a collision, and either the residual energy is spent in a wave process, or additional secondary solitons can form if the energy is sufficient. Qualitatively different scenarios of this interaction depend on the relative velocity of collision. Elements of visualizing nonlinear wave processes via shadowgraphy are discussed.     

Waveguides Induced by Screening-Photovoltaic Solitons in Biased Photorefractive-Photovoltaic Crystals

We investigate theoretically waveguides induced by screening-photovoltaic solitons in biased photorefractive-photovoltaic crystals. We show that the number of guided modes in a waveguide induced by a bright screening photovoltaic soliton increases monotonically with the increasing intensity ratio of the soliton, which is the ratio between the peak intensity of the soliton and the dark irradiance. On the other hand, waveguides induced by dark screening-photovoltaic solitons are always single mode for all intensity ratios and the confined energy near the centre of a dark screening-photovoltaic soliton increases monotonically with the increasing intensity ratio. When the bulk photovoltaic effect is neglectable, these waveguides are those induced by screening solitons. When the external field is absent, these waveguides predict those induced by photovoltaic solitons.     

Spinning particle-like solitons in superfluid3He-B

Particle-like topological solitons in superfluid³He-B are studied. The existing treatment of such objects indicates that static solitons have a free energy proportional to their size. They are thus unstable and will shrink to zero size. In the present work we consider spinning solitons whose size originates from an angular momentum barrier. In order for the solitons to be meaningfully described by theB phase their free energy must be small compared with their condensation energy. This requires that the angular momentum be large and effectively they are in the classical continuum limit. A detailed consideration of the variational procedure required to determine the soliton profile is presented allowing estimates of their size and energy. Address as from October 1991: Physics Institute, Faculty of Liberal Arts, Shizuoka University, Shizuoka 422, Japan     

Quantization of the chiral soliton in medium

Chiral solitons coupled with quarks in medium are studied based on the Wigner–Seitz approximation. The chiral quark soliton model is used to obtain the classical soliton solutions. To investigate nucleon and Δ in matter, the semi-classical quantization is performed by the cranking method. The saturation for nucleon matter and Δ matter are observed.     

Moving bright solitons in a pseudo-spin polarization Bose-Einstein condensate

We study the moving bright solitons in the weak attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schr ?dinger equation with the variational method and the imaginary time evolution method,two kinds of solitons(plane wave soliton and stripe solitons) are found in different parameter regions. It is shown that the soliton speed dominates its structure. The detuning between the Raman beam and energy states of the atoms decides the spin polarization strength of the system. The soliton dynamics is also studied for various moving speed and we find that the shape of individual components can be kept when the speed of soliton is low.     

Soliton interaction in the coupled mixed derivative nonlinear Schrödinger equations

The bright one- and two-soliton solutions of the coupled mixed derivative nonlinear Schrödinger equations in birefringent optical fibers are obtained by using the Hirota's bilinear method. The investigation on the collision dynamics of the bright vector solitons shows that there exists complete or partial energy switching in this coupled model. Such parametric energy exchanges can be effectively controlled and quantificationally measured by analyzing the collision dynamics of the bright vector solitons. The influence of two types of nonlinear coefficient parameters on the energy of each vector soliton, is also discussed. Based on the significant energy transfer between the two components of each vector soliton, it is feasible to exploit the future applications in the design of logical gates, fiber directional couplers and quantum information processors.     

Multi-hump bright solitons in a Schrödinger–mKdV system

We consider the problem of energy transport in a Davydov model along an anharmonic crystal medium obeying quartic longitudinal interactions corresponding to rigid interacting particles. The Zabusky and Kruskal unidirectional continuum limit of the original discrete equations reduces, in the long wave approximation, to a coupled system between the linear Schrödinger (LS) equation and the modified Korteweg–de Vries (mKdV) equation. Single- and two-hump bright soliton solutions for this LS–mKdV system are predicted to exist by variational means and numerically confirmed. The one-hump bright solitons are found to be the anharmonic supersonic analogue of the Davydov's solitons while the two-hump (in both components) bright solitons are found to be a novel type of soliton consisting of a two-soliton solution of mKdV trapped by the wave function associated to the LS equation. This two-hump soliton solution, as a two component solution, represents a new class of polaron solution to be contrasted with the two-soliton interaction phenomena from soliton theory, as revealed by a variational approach and direct numerical results for the two-soliton solution.     

Changes of properties of the soliton with temperature under influences of structure disorder in the α-helix protein molecules with three channels

The changes of property of solitons in α-helix protein molecules with three channels under influences of fluctuations of structure parameters and thermal perturbation of medium are extensively investigated using dynamic equations in the improved theory, numerical simulation and Runge-Kutta method. In this investigation the peculiarities of the solitons are given first in the motions of short-time and long-time and its collision features at T = 0 K and biological temperature T = 300 K. This study shows that the solutions of dynamic equations are solitons, which are very stable at T = 0 and 300 K, although its amplitudes and velocity are somewhat decreased relative to that at T = 0 K, the soliton can transport over 1000 amino acid residues, its lifetime is, at least, 120 ps. Subsequently, studies are made of the changes of properties of the soliton with variations of temperature of the medium and fluctuations of structure parameters including mass sequence of amino acid residues and the coupling constant, force constant, dipole–dipole interaction, chain–chain interaction and ground state energy in the α-helix proteins. The investigations indicate that the soliton has high thermal stability and can transport along the molecular chains retaining amplitude, energy and velocity, although the fluctuations of the structure parameters and temperature of the medium increase continually. However, the solitons disperse in larger fluctuations at T = 300 K and higher temperatures than 315 K. Thus it is determined that the critical temperature of the soliton is 315 K. Finally reasons are given for the generation of high thermal stability of the soliton and the correctness of the improved model is demonstrated. It is concluded that the soliton in the improved model is very robust against structure disorder and thermal perturbation of the α-helix protein molecules at 300 K, and is a possible carrier of bio-energy transport, and the improved model is maybe a candidate for the mechanism of this transport.     

光纤中飞秒孤子传输的量子理论

导出了光孤子系统的微观哈密顿量,用所给哈密顿量及色散关系导出了飞秒孤子在光纤中传输所满足的修正非线性薛定谔方程,用Hartree近似方法求解了所得方程,并研究了孤子的量子特征及经典过渡。结果表明,光纤中光场算符的量子力学平均为一系列有修正项的经典孤子的叠加,光场算符的准概率密度呈自压缩效应,压缩效果与高阶项的大小有关。 关键词：     

Solitons in photovoltaic photorefractive media with an external electric field

We use the classical Lie-group method for studying the evolution equation in photovoltaic photorefractive media with an external electric field, reducing it to some similarity equations firstly, and then obtain some exact analytical solutions including the soliton solution, the period solution and the oscillatory solution. We also obtain the bright soliton, dark soliton, gray soliton from these similarity equations with the numerical method. Furthermore, we investigate what factors contribute to the beamwidth of these solitons with the numerical method and know the beamwidth of these solitons are associated with the external electric field, the photovoltaic field and the intensity ratio of the incident soliton.     

Motion characteristics of Bragg grating solitons in rectangle-apodized fiber Bragg gratings

We introduce both concave and convex rectangular apodizations in the middle of fiber Bragg gratings to achieve slow light. Based on the nonlinear coupled mode equations (NLCMEs), the transmission characteristics of grating solitons in rectangle-apodized gratings are numerically simulated and analyzed. The rectangular apodization can change the grating coupling coefficient to give rise to slow and capture the solitons in gratings. The effects of the soliton energy parameters, the width of rectangular apodization and the variation of the coupling coefficient on the soliton transmission are presented. The results show that, the velocity of solitons can be slowed down, and the capability to capture a soliton depends on the energy of input solitons, coupling coefficient, and the rectangular width. Two kinds of soliton capture methods are proposed and compared with each other.     

Stabilization of the Soliton Transported Bio-energy in Protein Molecules in the Improved Model

We study the stabilization of the soliton transported bio-energy by the dynamic equations in the improved Davydov theory from four aspects containing the feature of free motion and states of the soliton at the long-time motion and at biological temperature 300 K and behaviors of collision of the solitons by Runge-Kutta method and physical parameter values appropriate to the $\alpha$-helix protein molecules. We prove that the new solitons can move without dispersion at a constant speed retaining its shape and energy in free and long-time motions and can go through each other without scattering. If considering further influence of the temperature effect of heat bath on the soliton, it is still thermally stable at biological temperature 300 K and in a time as long as 300 ps and amino acid spacings as large as 400, which shows that the lifetime of the new soliton is at least 300 ps, which is consistent with analytic result obtained by quantum perturbation theory. These results exhibit that the new soliton is a possible carrier of bio-energy transport and the improved model is possibly a candidate for the mechanism of this transport.