Quantum coherent tunneling between two atomic-molecular Bose-Einstein condensates

We study the quantum coherent tunneling dynamics of two weakly coupled atomic-molecular Bose-Einstein condensates (AMBEC). A weak link is supposed to be provided by a double-well trap. The regions of parameters where the macroscopic quantum localization of the relative atomic population occurs are revealed. The different dynamical regimes are found depending on the value of nonlinearity, namely, coupled oscillations of population imbalance of atomic and molecular condensate, including irregular oscillations regions, and macroscopic quantum self trapping regimes. Quantum means and quadrature variances are calculated for population of atomic and molecular condensates and the possibility of quadrature squeezing is shown via stochastic simulations within P-positive phase space representation method. Linear tunnel coupling between two AMBEC leads to correlations in quantum statistics.Received: 22 May 2004, Published online: 10 August 2004PACS: 03.75.-b Matter waves - 03.75.Gg Entanglement and decoherence in Bose-Einstein condensates - 03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations - 05.30.Jp Boson systems     

Amplification of matter rogue waves and breathers in quasi-two-dimensional Bose-Einstein condensates

We construct rogue wave and breather solutions of a quasi-two-dimensionalGross-Pitaevskii equation with a time-dependent interatomic interaction and external trap.We show that the trapping potential and an arbitrary functional parameter that present inthe similarity transformation should satisfy a constraint for the considered equation tobe integrable and yield the desired solutions. We consider two different forms offunctional parameters and investigate how the density of the rogue wave and breatherprofiles vary with respect to these functional parameters. We also construct vectorlocalized solutions of a two coupled quasi-two-dimensional Bose-Einstein condensatesystem. We then investigate how the vector localized density profiles modify in theconstant density background with respect to the functional parameters. Our results mayhelp to manipulate matter rogue waves experimentally in the two-dimensional Bose-Einsteincondensate systems.     

Disturbance and repair of solitary waves in blood vessels with aneurysm

This paper analyzes the effects of a local increase of radius followed by local variation of the thickness or rigidity of an elastic tube on the behavior of solitary waves. The basic equations for the analysis is a set of Boussinesq-type equations derived from the flow equations in elastic tubes. It is found that the increase in rigidity and thickness reduces the effects of the tube local enlargement on the amplitude of waves. Attention is paid to the aneurysmal affection of blood vessels where there is an increase in rigidity due to calcification or an increase of thickness due to thromboses. It thus comes that those effects contribute to the regeneration of blood waves and can merge the effects of the disease.     

On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients

We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique. We transform the two-dimensional two coupled variable coefficients nonlinear Schrödinger equations into Manakov equation with a constraint that connects diffraction and gain parameters with nonlinearity parameter. We investigate the characteristics of the constructed vector rogue wave solutions with four different forms of diffraction parameters. We report some interesting patterns that occur in the rogue wave structures. Further, we construct vector dark rogue wave solutions of the two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients and report some novel characteristics that we observe in the vector dark rogue wave solutions.     

On the particular solutions of an integrable equation governing short waves in a long-wave model

In this paper, we study Lie symmetries and similarity reductions of an integrable equation governing short waves in a long-wave model, derived recently by Faquir et al [M.J. Faquir, M.A. Manna, A. Neveu, Proc. R. Soc. A 463 (2007) 1939]. We present explicit solutions for this model for the first time, for the different choices of the physical parameter $\gamma$.     

Nonlinear short-wave propagation in ferrites

In this paper we discuss the propagation of nonlinear electromagnetic short waves in ferromagnetic insulators. We show that such propagation is perpendicular to an externally applied field. In the nonlinear regime we determine various possible propagation patterns: an isolated pulse, a modulated sinusoidal wave, and an asymptotic two-peak wave. The mathematical structure underlying the existence of these solutions is that of the integrable sine-Gordon equation.     

Asymptotic soliton train solutions of Kaup–Boussinesq equations

Asymptotic soliton trains arising from a ‘large and smooth’ enough initial pulse are investigated by the use of the quasiclassical quantization method for the case of Kaup–Boussinesq shallow water equations. The parameter varying along the soliton train is determined by the Bohr–Sommerfeld quantization rule which generalizes the usual rule to the case of ‘two potentials’ h₀(x) and u₀(x) representing initial distributions of height and velocity, respectively. The influence of the initial velocity u₀(x) on the asymptotic stage of the evolution is determined. Excellent agreement of numerical solutions of the Kaup–Boussinesq equations with predictions of the asymptotic theory is found.     

Boussinesq-type system of equations in the Bénard-Marangoni system

A system of coupled evolution equations for the bulk velocity and the surface displacement is found to govern the longwavelength perturbations in a Bénard-Marangoni system. This system of equations, involving nonlinearity, dispersion, and dissipation, is a generalization of the usual Boussinesq system.Instituto de Física Teórica, Universidade Estadual, Paulista, Rua Pamplona 145, 01405-900 São Paulo SP, Brazil. Laboratoire de Physique Mathématique, Université de Montpellier II, 34095 Montpellier Cedex 05, France. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp. 419–427, June, 1994.     

Population persistence in weakly-coupled sinks

We consider a single species population obeying a saturated growth model with spatial diffusion taken into account explicitly. Strong spatial heterogeneity is considered, represented by a position dependent reproduction rate. The geometry of the problem is that of two patches where the reproductive rate is positive, surrounded by unfavorable patches where it is negative. We focus on the particular case where the population would not persist in the single patches (sinks). We find by means of an analytical derivation, supplemented by a numerical calculation, the conditions for the persistence of the population in the compound system of weakly connected patches. We show that persistence is possible even if each individual patch is a sink where the population would go extinct. The results are of particular relevance for ecological management at the landscape level, showing that small patches may harbor populations as long as the connectivity with adjacent patches is maintained. Microcosmos experiences with bacteria could be performed for experimental verification of the predictions.