Terms Of Solitons Research Articles

ATR-Infrared spectroscopic study of n-doped polyacetylene films

The attenuated total reflection infrared (ATR-IR) spectra oftrans-polyacetylene (trans-PA) film doped with sodium (n-doping) were observed in the range of 1900 to 700 cm−1. The observed IR bands were attributed to negatively charged domains created by n-doping electrons. The doping-induced IR bands showed considerable difference from its pristine film. After doping, the out-of-plane CH deformation band of the strong 1010 cm−1 region in the pristine film disappeared while several new bands were observed at 1600 (due to C=C stretching), 1400 (due to in-plane CH bending), 1290 and 1174 (due to CH stretching), and 880 cm−1 (due to CC stretching) regions for Nadoped PA. In particular, a weak band of C=C stretching at 1600 cm−1 was newly obtained for the first time in the present study. The electro conductivity of the dopedtrans-PA film was 102 S/cm and the origins of doping-induced IR bands are discussed in terms of solitons and polarons.

Three-dimensional Ricci solitons which project to surfaces

We study $3$-dimensional Ricci solitons which project via a semi-conformal mapping to a surface. We reformulate the equations in terms of parameters of the map; this enables us to give an ansatz for constructing solitons in terms of data on the surface. A complete description of the soliton structures on all the $3$-dimensional geometries is given, in particular, non-gradient solitons are found on Nil and Sol.

Bright Matter-Wave Soliton Collisions in a Harmonic Trap: Regular and Chaotic Dynamics

Collisions between bright solitary waves in the 1D Gross-Pitaevskii equation with a harmonic potential, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. A particle analogy for the solitary waves is formulated and shown to be integrable for a two-particle system. The extension to three particles is shown to support chaotic regimes. Good agreement is found between the particle model and simulations of the full wave dynamics, suggesting that the dynamics can be described in terms of solitons both in regular and chaotic regimes, presenting a paradigm for chaos in wave mechanics.

Gyroelectric cubic-quintic dissipative solitons

The influence of an externally applied magnetic field upon classic cubic quintic dissipative solitons is investigated using both exact simulations and a Lagrangian technique. The basic approach is to use a spatially inhomogeneous magnetic field and to consider two important geometries, namely the Voigt and the Faraday effects. A layered structure is selected for the Voigt case, with the principal aim being to demonstrate nonreciprocal behavior for various classes of spatial solitons that are known to exist as solutions of the complex Ginzburg-Landau cubic-quintic envelope equation under dissipative conditions. The system is viewed as dynamical, and we display the behavior patterns of the spatial solitons in terms of two-dimensional dynamical plots involving the total energy and the peak amplitude of the spatial solitons. This leads to limit cycle plots that beautifully reveal the behavior of the solitons solutions at all points along the propagation axis. The closed contour that exists in the absence of a magnetic field is opened up, and a limit point is exposed. The onset of chaos is revealed in a dramatic way, and it is clear that detailed control by the external magnetic field can be exercised. The Lagrangian approach is adjusted to deal with dissipative systems, and through the choice of particular trial functions, aspects of the dynamic behavior of the spatial are predicted by this approach. Finally, some vortex dynamics in the Faraday configuration are investigated.

Identifying Diffusion Processes in One-Dimensional Lattices in Thermal Equilibrium

In this Letter, I propose that a properly rescaled spatiotemporal correlation function of the energy density fluctuations may be applied to characterize the equilibrium diffusion processes in lattice systems with finite temperature. Applying this function, the diffusion processes in three one-dimensional nonlinear lattices are studied. The diffusion exponent is shown to be related to the diverging exponent of the thermal conductivity of a lattice through the relation , as has been proved based on the Lévy walk assumption. The diffusion behavior is explained in terms of solitons and phonons.

Solitary waves in self-gravitating molecular clouds

Molecular clouds are self-gravitating fluids that support different waves and contain highly nonlinear clumps and filaments, for which explanations have been sought in terms of solitons. The present paper explores the possibility that several (neutral) species with different thermal speeds coexist, as in a molecular cloud consisting of gas and dust, or of a mixture of normal matter and dark matter. It is shown that this model can support soliton formation, both with humps or dips in the self-gravitational potential. The existence domain has been given in terms of the hot species Mach number and fractional mass density, in a gas-dynamic description which emphasizes the constraints coming from the sonic and neutral points, and from the limits due to infinite compression or total rarefaction. One species is compressed while the other is rarefied, allowing the system to reach a mass neutral point outside equilibrium. In this way, solitons are possible without invoking interaction with a weakly ionized cloud component or involving envelope solitons that are not really stationary structures.

The Interaction Energy of Well-Separated Skyrme Solitons

We prove that the asymptotic field of a Skyrme soliton of any degree has a non-trivial multipole expansion. It follows that every Skyrme soliton has a well-defined leading multipole moment. We derive an expression for the linear interaction energy of well-separated Skyrme solitons in terms of their leading multipole moments. This expression can always be made negative by suitable rotations of one of the Skyrme solitons in space and iso-space.We show that the linear interaction energy dominates for large separation if the orders of the Skyrme solitons' multipole moments differ by at most two. In that case there are therefore always attractive forces between the Skyrme solitons.

Toward single-cycle laser systems

Few-cycle pulse generation based on Ti:sapphire, Cr:forsterite, and Cr:YAG gain media is reviewed. The dynamics of these laser systems is well understood in terms of soliton and dispersion managed soliton formation stabilized by artificial saturable absorber action provided by Kerr-lens modelocking. These systems generate 5-, 14-, and 20-fs pulses with spectral coverages of 600-1150, 1100-1600, and 1200-1500 nm, respectively. The design of dispersion compensating laser optics providing high reflectivity and prismless operation over this bandwidth is discussed. A novel active synchronization scheme based on balanced optical cross correlation, the equivalent to balanced microwave detection, for synchronization of independently mode-locked lasers is introduced. Its use in synchronizing an octave-spanning Ti:sapphire laser and a 30-fs Cr:forsterite laser yields 300 attoseconds timing jitter measured from 10 mHz to 2.3 MHz. The spectral overlap between the two lasers is large enough to enable direct detection of the difference in the carrier-envelope offset frequency between the two lasers. These are the most important steps in the synthesis of single-cycle optical pulses with spectra spanning 600-1600 nm.

The loop group ofE8andK-theory from 11d

We examine the conjecture that an 11d E_8 bundle, appearing in the calculation of phases in the M-Theory partition function, plays a physical role in M-Theory, focusing on consequences for the classification of string theory solitons. This leads for example to a classification of IIA solitons in terms of that of LE_8 bundles in 10d. Since K(Z,2) approximates LE_8 up to \pi_{14}, this reproduces the K-Theoretic classification of IIA D-branes while treating NSNS and RR solitons more symmetrically and providing a natural interpretation of G_0 as the central extension of LE_8.

The 1320-nm excited FT-Raman spectra of lightly iodine-dopedtrans-polyacetylene

The FT-Raman spectra oftrans-polyacetylene films doped lightly with iodine were obtained with the 1320-nm laser line. The observed Raman bands are attributed to positively charged domains created by acceptor doping. The observed Raman wavenumbers of the ν2 (CC stretch), ν3 and ν4 bands (mixed of CC stretch and CH in-plan bending)|of iodine-doped form are slightly higher than those of the corresponding bands of pristinetrans-polyacetylene, whereas the contrary is the case for ν1 band (C=C stretch)|of iodine-doped form. In particular, these upshifts of the ν2 and ν3 bands are distinguished from the downshifts of these bands in donor doping. The origin of doping induced Raman bands is discussed in terms of solitons and polarons.

The soliton solution of BBGKY'S chain of quantum kinetic equations for system of particles, interacting by delta potential

The BBGKY's chain of quantum kinetic equations that describes the system of particles interacting by delta potential is solved with the help of nonlinear Schrödinger's equations. The solution of the chain is defined in terms of soliton.

Statics and dynamics of a one-dimensional quantum many-body system

The macroscopic zero-temperature behavior of weakly incommensurate systems in one dimension is described in terms of solitons. The soliton density n obeys equations displaying several types of singular interfacelike solutions: (i) equilibrium or moving boundary between the $n=0$ and finite n regions, and (ii) stationary or moving annihilation front separating solitons from antisolitons.

An interpretation of the energy variations of dispersion managed solitons in terms of effective average dispersion

We show that the variation in dispersion managed soliton energy that occurs as the amplifier position varies within the dispersion map, for a fixed map strength, can be interpreted using the concept of effective average dispersion. Using this concept we physically explain why the location of the amplifier can produce a greater or lesser energy enhancement factor than the lossless model.

How Bob Laughlin tamed the giant graviton from Taub-NUT space

In this paper we show how two dimensional electron systems can be modeled by strings interacting with D-branes. The dualities of string theory allow several descriptions of the system. These include descriptions in terms of solitons in the near horizon D6-brane theory, non-commutative gauge theory on a D2-brane, the Matrix Theory of D0-branes and finally as a giant graviton in M-theory. The soliton can be described as a D2-brane with an incompressible fluid of D0-branes and charged string-ends moving on it. Including an NS5 brane in the system allows for the existence of an edge with the characteristic massless chiral edge states of the Quantum Hall system.

Impact of polarisation-mode dispersion in dispersion-managed soliton systems

Since enhanced power solitons are usually applied in dispersion-managed soliton systems, it might be expected that dispersion-managed solitons have a stronger resistance to polarisation-mode dispersion than conventional solitons. However, it is shown that dispersion-managed solitons behave similarly to conventional solitons in terms of resistance to polarisation-mode dispersion.

No saturation of the quantum Bogomolnyi bound by two-dimensional N = 1 supersymmetric solitons

We reanalyse the question whether the quantum Bogomolnyi bound is saturated in the two-dimensional supersymmetric kink and sine-Gordon models. Our starting point is the usual expression for the one-loop correction to the mass of a soliton in terms of sums over zero-point energies. To regulate these sums, most authors put the system in a box with suitable boundary conditions, and impose an ultraviolet cut-off. We distinguish between an energy cut-off and a mode-number cut-off, and show that they lead to different results. We claim that only the mode cut-off yields correct results, and only if one considers exactly the same number of bosonic and fermionic modes in the total sum over bound-state and zero-point energies. To substantiate this claim, we show that in the sine-Gordon model only the mode cut-off yields a result for the quantum soliton mass that is consistent with the exact result for the spectrum as obtained by Dashen et al. from quantising the so-called breather solution. In the supersymmetric case, our conclusion is that contrary to previous claims the quantum Bogomolnyi bound is not saturated in any of the two-dimensional models considered.

The 1320-nm excited FT-Raman spectra of Na-doped trans-polyacetylene

The FT-Raman spectra of trans-polyacetylene doped with Na at various concentrations were observed with the 1320-nm laser line. Doping-induced Raman bands for lightly doped trans-polyacetylene were observed for the first time. The observed wavenumbers of the ν 1 and ν 4 bands (C=C and C=C stretches) of lightly doped trans-polyacetylene are lower than those of the corresponding bands of pristine trans-polyacetylene, whereas the contrary is the case for heavily doped trans-polyacetylene. The origins of doping-induced Raman bands are discussed in terms of solitons and polarons.

No saturation of the quantum Bogomolnyi bound by two-dimensional N = 1 supersymmetric solitons

We reanalyse the question whether the quantum Bogomolnyi bound is saturated in the two-dimensional supersymmetric kink and sine-Gordon models. Our starting point is the usual expression for the one-loop correction to the mass of a soliton in terms of sums over zero-point energies. To regulate these sums, most authors put the system in a box with suitable boundary conditions, and impose an ultraviolet cut-off. We distinguish between an energy cut-off and a mode number cut-off, and show that they lead to different results. We claim that only the mode cut-off yields correct results, and only if one considers exactly the same number of bosonic and fermionic modes in the total sum over bound-state and zero-point energies. To substantiate this claim, we show that in the sine-Gordon model only the mode cut-off yields a result for the quantum soliton mass that is consistent with the exact result for the spectrum as obtained by Dashen et al. from quantising the so-called breather solution. In the supersymmetric case, our conclusion is that contrary to previous claims the quantum Bogomolnyi bound is not saturated in any of the two-dimensional models considered.

Soliton in discrete and continuum alpha helical proteins with higher-order excitations

We consider discrete and continuum models of alpha helical proteins with different orders of molecular excitations and interactions. In both the cases integrable models were identified for specific choice of parameters and the elementary excitations expressed in terms of solitons. Also, equivalent integrable Heisenberg spin systems were obtained.

Curvature-induced geometrical frustration in magnetic systems

We study classical Heisenberg spins in the continuum limit (i.e., the nonlinear \ensuremath{\sigma} model) on an elastic two-dimensional manifold with at least one nonconstant principal curvature. If the corresponding Euler-Lagrange equations support a soliton solution, the nonconstant curvature of the geometry induces geometrical frustration in the region of the soliton which is relieved by a deformation of the manifold in the region of the soliton. We illustrate these results on an elliptic cylinder where we find an elastic soliton in terms of the variable ellipticity along the axis of the cylinder.