We consider, by means of the variational approximation ͑VA͒ and direct numerical simulations of the Gross-Pitaevskii ͑GP͒ equation, the dynamics of two-dimensional ͑2D͒ and 3D condensates with a scattering length containing constant and harmonically varying parts, which can be achieved with an ac magnetic field tuned to the Feshbach resonance. For a rapid time modulation, we develop an approach based on the direct averaging of the GP equation, without using the VA. In the 2D case, both VA and direct simulations, as well as the averaging method, reveal the existence of stable self-confined condensates without an external trap, in agreement with qualitatively similar results recently reported for spatial solitons in nonlinear optics. In the 3D case, the VA again predicts the existence of a stable self-confined condensate without a trap. In this case, direct simulations demonstrate that the stability is limited in time, eventually switching into collapse, even though the constant part of the scattering length is positive ͑but not too large͒. Thus a spatially uniform ac magnetic field, resonantly tuned to control the scattering length, may play the role of an effective trap confining the condensate, and sometimes causing its collapse.

The theory of optical dispersive shocks generated in the propagation of light beams through photorefractive media is developed. A full one-dimensional analytical theory based on the Whitham modulation approach is given for the simplest case of a sharp steplike initial discontinuity in a beam with one-dimensional striplike geometry. This approach is confirmed by numerical simulations, which are extended also to beams with cylindrical symmetry. The theory explains recent experiments where such dispersive shock waves have been observed.

We consider formation of dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms. It is shown that for big enough initial inhomogeneity of density, interplay of nonlinear and dispersion effects leads to wave breaking phenomenon followed by generation of a train of dark solitons. Analytical theory is confirmed by numerical simulations. Experiments on free expansion of Bose-Einstein condensate (BEC) have shown [1] that evolution of large and smooth distributions of BEC is described very well by hydrodynamic approximation [2] where dispersion and dissipation effects are neglected. At the same time, it is well known from classical compressible gas dynamics (see, e.g., [3]) that typical initial distributions of density and velocity can lead to wave breaking phenomenon when formal solution of hydrodynamical equations becomes multivalued. It means that near the wave breaking point one cannot neglect dispersion and/or dissipation effects which prevent formation of a multivalued region of a solution. If the dissipation effects dominate the dispersion ones, then the multivalued region is replaced by the classical shock, i.e., narrow layer with strong dissipation within, which separates smooth regions with different values of density, fluid velocity and other physical parameters. This situation was studied in classical gas dynamics and found many practical applications. If, however, the dispersion effects dominate dissipation ones, then the region of strong oscillations is generated in the vicinity of the wave breaking point [4,5]. Observation of dark solitons in BEC [6][7][8] shows that the main role in dynamics of BEC is played by dispersion and nonlinear effects taken into account by the standard Gross-Pitaevskii (GP) equation [9], and dissipation effects are relatively small and can be considered as perturbation. Hence, there are initial distributions of BEC which can lead to formation of dissipationless shock waves. Here we shall consider such a possibility.The starting point of our consideration is the fact that the sound velocity in BEC is proportional to the square root from its density (see, e.g., [9] and references therein). Thus, if we create inhomogeneous BEC with high density hump (with density ϳ 1 ) in the center of lower density distribution (with density ϳ 0 ), and after that release this central part of BEC, then the high density hump will tend to expand with velocity ϳ ͱ 1 greater than the sound velocity ϳ ͱ 0 of propagation of disturbance in lower density BEC. As a result, wave breaking and formation of dissipationless shock wave can occur in this case. Note that initial distributions of this type were realized in experiment [10] on measurement of sound velocity in BEC and in the recent experiment [11]. In [10] the hump's density 1 was too small to generate shocks (see below). In experiment [11] generation of shock oscillations was apparently observed.The theory of dissipationless shock waves in media described by a one-dimensional (1D) nonlinear Schrödinger (NLS...

Asymptotic behavior of initially ''large and smooth'' pulses is investigated at two typical stages of their evolution governed by the defocusing nonlinear Schrödinger equation. At first, wave breaking phenomenon is studied in the limit of small dispersion. A solution of the Whitham modulational equations is found for the case of dissipationless shock wave arising after the wave breaking point. Then, asymptotic soliton trains arising eventually from a large and smooth initial pulse are studied by means of a semiclassical method. The parameter varying along the soliton train is calculated from the generalized Bohr-Sommerfeld quantization rule, so that the distribution of eigenvalues depends on two functions-intensity 0 (x) of the initial pulse and its initial chirp v 0 (x). The influence of the initial chirp on the asymptotic state is investigated. Excellent agreement of the numerical solution of the defocusing NLS equation with predictions of the asymptotic theory is found.

The modulational instability of gravity wave trains on the surface of water acted upon by wind and under influence of viscosity is considered. The wind regime is that of validity of Miles' theory and the viscosity is small. By using a perturbed nonlinear Schrödinger equation describing the evolution of a narrow-banded wavepacket under the action of wind and dissipation, the modulational instability of the wave group is shown to depend on both the frequency (or wavenumber) of the carrier wave and the strength of the friction velocity (or the wind speed). For fixed values of the watersurface roughness, the marginal curves separating stable states from unstable states are given. It is found in the low-frequency regime that stronger wind velocities are needed to sustain the modulational instability than for high-frequency water waves. In other words, the critical frequency decreases as the carrier wave age increases. Furthermore, it is shown for a given carrier frequency that a larger friction velocity is needed to sustain modulational instability when the roughness length is increased.

Background Plasmodium vivax is a widely distributed, neglected parasite that can cause malaria and death in tropical areas. It is associated with an estimated 80–300 million cases of malaria worldwide. Brazilian tropical rain forests encompass host- and vector-rich communities, in which two hypothetical mechanisms could play a role in the dynamics of malaria transmission. The first mechanism is the dilution effect caused by presence of wild warm-blooded animals, which can act as dead-end hosts to Plasmodium parasites. The second is diffuse mosquito vector competition, in which vector and non-vector mosquito species compete for blood feeding upon a defensive host. Considering that the World Health Organization Malaria Eradication Research Agenda calls for novel strategies to eliminate malaria transmission locally, we used mathematical modeling to assess those two mechanisms in a pristine tropical rain forest, where the primary vector is present but malaria is absent.Methodology/Principal FindingsThe Ross–Macdonald model and a biodiversity-oriented model were parameterized using newly collected data and data from the literature. The basic reproduction number () estimated employing Ross–Macdonald model indicated that malaria cases occur in the study location. However, no malaria cases have been reported since 1980. In contrast, the biodiversity-oriented model corroborated the absence of malaria transmission. In addition, the diffuse competition mechanism was negatively correlated with the risk of malaria transmission, which suggests a protective effect provided by the forest ecosystem. There is a non-linear, unimodal correlation between the mechanism of dead-end transmission of parasites and the risk of malaria transmission, suggesting a protective effect only under certain circumstances (e.g., a high abundance of wild warm-blooded animals).Conclusions/SignificanceTo achieve biological conservation and to eliminate Plasmodium parasites in human populations, the World Health Organization Malaria Eradication Research Agenda should take biodiversity issues into consideration.

The variant of concern (VOC) P.1 emerged in the Amazonas state (Brazil) and was sequenced for the 1st time on 6-Jan-2021 by the Japanese National Institute of Infectious Diseases. It contains a constellation of mutations, ten of them in the spike protein. Consequences of these mutations at the populational level have been poorly studied so far. From December-2020 to February-2021, Manaus was devastated by four times more cases compared to the previous peak (April-2020). Here, data from the national health surveillance of hospitalized individuals were analysed using a model-based approach to estimate P.1 parameters of transmissibility and reinfection by maximum likelihood. Sensitivity analysis was performed changing pathogenicity and the period analysed (including/excluding the health system collapse period). In all analysed cases, the new variant transmissibility was found to be about 2.5 times higher compared to the previous variant in Manaus. A low probability of reinfection by the new variant (6.4%) was estimated, even under initial high prevalence (68%) by the time P.1 emerged. Consequences of a higher transmissibility were already observed with VOC B.1.1.7 in the UK and Europe. Urgent measures must be taken to control the spread of P.1.

By using the multiple scale method with the simultaneous introduction of multiple times, we study the propagation of long surface-waves in a shallow inviscid fluid. As a consequence of the requirements of scale invariance and absence of secular terms in each order of the perturbative expansion, we show that the Korteweg-de Vries hierarchy equations do appear in the description of such waves. Finally, we show that this procedure of eliminating secularities is closely related to the renormalization technique introduced by Kodama and Taniuti. 03.40.Kf ; 47.35.+i ; 03.40.Gc