Stable and mobile excited two-dimensional dipolar Bose-Einstein condensate solitons

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Quantum Aspects of Solitons and Deformations on Ad'S IND. 4'x C'P POT.3' ('S POT. 7')

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Solitons in atomic condensates, with optical lattices and field-induced dipole moments

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Vector solitons in a spin-orbit-coupled spin-2 Bose-Einstein condensate

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Entropic information for travelling solitons in Lorentz and CPT breaking systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Toroidal solitons in 3+1 dimensional integrable theories

We analyze the integrability properties of models defined on the symmetric space SU(2)/U(1) in 3 + 1 dimensions, using a recently proposed approach for integrable theories in any dimension. We point out the key ingredients for a theory to possess an infinite number of local conservation laws, and discuss classes of models with such property, We propose a 3 + 1-dimensional, relativistic invariant field theory possessing a toroidal soliton solution carrying a unit of topological charge given by the Hopf map. Construction of the action is guided by the requirement that the energy of static configuration should be scale invariant. The solution is constructed exactly. The model possesses an infinite number of local conserved currents. The method is also applied to the Skyrme-Faddeev model, and integrable submodels are proposed. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Hirota's solitons in the affine and the conformal affine Toda models

We use Hirota's method formulated as a recursive scheme to construct a complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two different types of degeneracies encountered in Hirota's perturbation approach. We also derive an universal mass formula for all Hirota's solutions to the affine Toda model valid for all underlying Lie groups. Embedding of the affine Toda model in the conformal affine Toda model plays a crucial role in this analysis.

Hirota method for oblique solitons in two-dimensional supersonic nonlinear Schrodinger flow

In a previous work El et al. (2006) [1] exact stable oblique soliton solutions were revealed in two-dimensional nonlinear Schrodinger flow. In this work we show that single soliton solution can be expressed within the Hirota bilinear formalism. An attempt to build two-soliton solutions shows that the system is "close" to integrability provided that the angle between the solitons is small and/or we are in the hypersonic limit. (C) 2012 Elsevier B.V. All rights reserved.

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

The existence and stability of three-dimensional (3D) solitons, in cross-combined linear and nonlinear optical lattices, are investigated. In particular, with a starting optical lattice (OL) configuration such that it is linear in the x-direction and nonlinear in the y-direction, we consider the z-direction either unconstrained (quasi-2D OL case) or with another linear OL (full 3D case). We perform this study both analytically and numerically: analytically by a variational approach based on a Gaussian ansatz for the soliton wavefunction and numerically by relaxation methods and direct integrations of the corresponding Gross-Pitaevskii equation. We conclude that, while 3D solitons in the quasi-2D OL case are always unstable, the addition of another linear OL in the z-direction allows us to stabilize 3D solitons both for attractive and repulsive mean interactions. From our results, we suggest the possible use of spatial modulations of the nonlinearity in one of the directions as a tool for the management of stable 3D solitons.

Helical buckling of Skyrme-Faddeev solitons

Solitons in the Skyrme-Faddeev model on R-2 x S-1 are shown to undergo buckling transitions as the circumference of the S-1 is varied. These results support a recent conjecture that solitons in this field theory are well-described by a much simpler model of elastic rods.

Solitons in nonlinear Schrödinger equations.

Using a mathematical approach accessible to graduate students of physics and engineering, we show how solitons are solutions of nonlinear Schrödinger equations. Are also given references about the history of solitons in general, their fundamental properties and how they have found applications in optics and fiber-optic communications.

Breeze-forced oscillations and strongly nonlinear tide-generated internal solitons

Programa de doctorado en Oceanografía

Quantum solitons in the XXZ model with staggered external magnetic field

The 1-D 1/2-spin XXZ model with staggered external magnetic field, when restricting to low field, can be mapped into the quantum sine-Gordon model through bosonization: this assures the presence of soliton, antisoliton and breather excitations in it. In particular, the action of the staggered field opens a gap so that these physical objects are stable against energetic fluctuations. In the present work, this model is studied both analytically and numerically. On the one hand, analytical calculations are made to solve exactly the model through Bethe ansatz: the solution for the XX + h staggered model is found first by means of Jordan-Wigner transformation and then through Bethe ansatz; after this stage, efforts are made to extend the latter approach to the XXZ + h staggered model (without finding its exact solution). On the other hand, the energies of the elementary soliton excitations are pinpointed through static DMRG (Density Matrix Renormalization Group) for different values of the parameters in the hamiltonian. Breathers are found to be in the antiferromagnetic region only, while solitons and antisolitons are present both in the ferromagnetic and antiferromagnetic region. Their single-site z-magnetization expectation values are also computed to see how they appear in real space, and time-dependent DMRG is employed to realize quenches on the hamiltonian parameters to monitor their time-evolution. The results obtained reveal the quantum nature of these objects and provide some information about their features. Further studies and a better understanding of their properties could bring to the realization of a two-level state through a soliton-antisoliton pair, in order to implement a qubit.

Interaction of spatially overlapping standing electromagnetic solitons in plasmas

Numerical investigations on mutual interactions between two spatially overlapping standing electromagnetic solitons in a cold unmagnetized plasma are reported. It is found that an initial state comprising of two overlapping standing solitons evolves into different end states, depending on the amplitudes of the two solitons and the phase difference between them. For small amplitude solitons with zero phase difference, we observe the formation of an oscillating bound state whose period depends on their initial separation. These results suggest the existence of a bound state made of two solitons in the relativistic cold plasma fluid model.