Two Dimensional Large Amplitude Quasi Solitons in Thin Helium Films

Large amplitude local density fluctuations in a thin superfluid He film is considered. It is shown that these large amplitude fluctuations travel and behave like "quasi-solitons" under collision, even when the full nonlinearity arising from the Van der Waals potential is taken into account.

Bright solitons in a quasi-one-dimensional reduced model of a dipolar Bose-Einstein condensate with repulsive short-range interactions

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Soliton's eigenvalue based analysis on the generation mechanism of rogue wave phenomenon in optical fibers exhibiting weak third order dispersion

One of the extraordinary aspects of nonlinear wave evolution which has been observed as the spontaneous occurrence of astonishing and statistically extraordinary amplitude wave is called rogue wave. We show that the eigenvalues of the associated equation of nonlinear Schrödinger equation are almost constant in the vicinity of rogue wave and we validate that optical rogue waves are formed by the collision between quasi-solitons in anomalous dispersion fiber exhibiting weak third order dispersion.

Dynamics of quasi-one-dimensional bright and vortex solitons of a dipolar Bose-Einstein condensate with repulsive atomic interaction

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The dynamics of bright matter wave solitons in a quasi one-dimensional Bose-Einstein condensate with a rapidly varying trap

The dynamics of a bright matter wave soliton in a quasi one-dimensional Bose-Einstein condensate (BEC) with a periodically rapidly varying time trap is considered. The governing equation is based on averaging the fast modulations of the Gross-Pitaevskii (GP) equation. This equation has the form of a GP equation with an effective potential of a more complicated structure than an unperturbed trap. In the case of an inverted (expulsive) quadratic trap corresponding to an unstable GP equation, the effective potential can be stable. For the bounded space trap potential it is showed that bifurcation exists, i.e. the single-well potential bifurcates to the triple-well effective potential. The stabilization of a BEC cloud on-site state in the temporary modulated optical lattice is found. This phenomenon is analogous to the Kapitza stabilization of an inverted pendulum. The analytical predictions of the averaged GP equation are confirmed by numerical simulations of the full GP equation with rapid perturbations.

Bright solitons in quasi-one-dimensional dipolar condensates with spatially modulated interactions

We introduce a model for the condensate of dipolar atoms or molecules, in which the dipole-dipole interaction (DDI) is periodically modulated in space due to a periodic change of the local orientation of the permanent dipoles, imposed by the corresponding structure of an external field (the necessary field can be created, in particular, by means of magnetic lattices, which are available to the experiment). The system represents a realization of a nonlocal nonlinear lattice, which has a potential to support various spatial modes. By means of numerical methods and variational approximation (VA), we construct bright one-dimensional solitons in this system and study their stability. In most cases, the VA provides good accuracy and correctly predicts the stability by means of the Vakhitov-Kolokolov criterion. It is found that the periodic modulation may destroy some solitons, which exist in the usual setting with unmodulated DDI and can create stable solitons in other cases, not verified in the absence of modulations. Unstable solitons typically transform into persistent localized breathers. The solitons are often mobile, with inelastic collisions between them leading to oscillating localized modes. © 2013 American Physical Society.

Bright solitons in a quasi-one-dimensional dipolar Bose-Einstein condensate

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Ring Dark Solitons in Toroidal Bose-Einstein Condensates

In this Thesis, we study various aspects of ring dark solitons (RDSs) in quasi-two-dimensional toroidally trapped Bose-Einstein condensates, focussing on atomic realisations thereof. Unlike the well-known planar dark solitons, exact analytic expressions for RDSs are not known. We address this problem by presenting exact localized soliton-like solutions to the radial Gross-Pitaevskii equation. To date, RDSs have not been experimentally observed in cold atomic gases, either. To this end, we propose two protocols for their creation in experiments. It is also currently well known that in dimensions higher than one, (ring) dark solitons are susceptible, in general, to an irreversible decay into vortex-antivortex pairs through the snake instability. We show that the snake instability is caused by an unbalanced quantum pressure across the soliton's notch, linking the instability to the Bogoliubov-de Gennes spectrum. In particular, if the angular symmetry is maintained (or the toroidal trapping is restrictive enough), we show that the RDS is stable (long-lived with a lifetime of order seconds) in two dimensions. Furthermore, when the decay does take place, we show that the snake instability can in fact be reversible, and predict a previously unknown revival phenomenon for the original (many-)RDS system: the soliton structure is recovered and all the point-phase singularities (i.e. vortices) disappear. Eventually, however, the decay leads to an example of quantum turbulence; a quantum example of the laminar-to-turbulent type of transition.

The concept of quasi-integrability: a concrete example

We use the deformed sine-Gordon models recently presented by Bazeia et al [1] to take the first steps towards defining the concept of quasi-integrability. We consider one such definition and use it to calculate an infinite number of quasi-conserved quantities through a modification of the usual techniques of integrable field theories. Performing an expansion around the sine-Gordon theory we are able to evaluate the charges and the anomalies of their conservation laws in a perturbative power series in a small parameter which describes the ""closeness"" to the integrable sine-Gordon model. We show that in the case of the two-soliton scattering the charges, up to first order of perturbation, are conserved asymptotically, i.e. their values are the same in the distant past and future, when the solitons are well separated. We indicate that this property may hold or not to higher orders depending on the behavior of the two-soliton solution under a special parity transformation. For closely bound systems, such as breather-like field configurations, the situation however is more complex and perhaps the anomalies have a different structure implying that the concept of quasi-integrability does not apply in the same way as in the scattering of solitons. We back up our results with the data of many numerical simulations which also demonstrate the existence of long lived breather-like and wobble-like states in these models.

SOME COMMENTS ON QUASI-INTEGRABILITY

In this paper we present our preliminary results which suggest that some field theory models are `almost` integrable; i.e. they possess a large number of `almost` conserved quantities. First we demonstrate this, in some detail, on a class of models which generalise sine-Gordon model in (1+1) dimensions. Then, we point out that many field configurations of these models look like those of the integrable systems and others are very close to being integrable. Finally we attempt to quantify these claims looking in particular, both analytically and numerically, at some long lived field configurations which resemble breathers.

Dynamics of bright matter-wave solitons in a Bose-Einstein condensate with inhomogeneous scattering length

We investigate dynamical effects of a bright soliton in Bose-Einstein condensed (BEC) systems with local and smooth space variations of the two-body atomic scattering length. It includes a discussion about the possible observation of a new type of standing nonlinear atomic matter wave in cigar-type traps. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. By considering an analytical time-dependent variational approach and also full numerical simulation of one-dimensional and three-dimensional Gross-Pitaevskii equations, we study processes such as trapping, reflection and transmission of the bright matter soliton due to the impurity. We also derive conditions for the collapse of the bright solitary wave, considering a quasi-one-dimensional BEC with attractive local inhomogeneity.

Black soliton in a quasi-one-dimensional trapped fermion-fermion mixture

Employing a time dependent mean-field-hydrodynamic model we study the generation of black solitons in a degenerate fermion-fermion mixture in a cigar-shaped geometry using variational and numerical solutions. The black soliton is found to be the first stationary vibrational excitation of the system and is considered to be a nonlinear continuation of the vibrational excitation of the harmonic oscillator state. We illustrate the stationary nature of the black soliton, by studying different perturbations on it after its formation.

Bright solitons in coupled defocusing NLS equation supported by coupling: Application to Bose-Einstein condensation

We demonstrate the formation of bright solitons in coupled self-defocusing nonlinear Schrodinger (NLS) equation supported by attractive coupling. As an application we use a time-dependent dynamical mean-field model to study the formation of stable bright solitons in two-component repulsive Bose-Einstein condensates (BECs) supported by interspecies attraction in a quasi one-dimensional geometry. When all interactions are repulsive, there cannot be bright solitons. However, bright solitons can be formed in two-component repulsive BECs for a sufficiently attractive interspecies interaction, which induces an attractive effective interaction among bosons of same type. (c) 2005 Elsevier B.V. All rights reserved.

Bright solitons and soliton trains in a fermion-fermion mixture

We use a time-dependent dynamical mean-field-hydrodynamic model to predict and study bright solitons in a degenerate fermion-fermion mixture in a quasi-one-dimensional cigar-shaped geometry using variational and numerical methods. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances there cannot be bright solitons for repulsive interspecies fermion-fermion interactions. However, stable bright solitons can be formed for a sufficiently attractive interspecies interaction. We perform a numerical stability analysis of these solitons and also demonstrate the formation of soliton trains. These fermionic solitons can be formed and studied in laboratory with present technology.

Three-dimensional solitons in cross-combined linear and nonlinear optical lattices

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