Soliton trains in Bose-Fermi mixtures

We theoretically consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases. While we assume the forces between atoms in a pure Bose component to be effectively repulsive, their character can be changed from repulsive to attractive in the presence of fermions provided the Bose and Fermi gases attract each other strongly enough. In such a regime the Bose component becomes a gas of effectively attractive atoms. Hence, generating bright solitons in the bosonic gas is possible. Indeed, after a sudden increase of the strength of attraction between bosons and fermions (realized by using a Feshbach resonance technique or by firm radial squeezing of both samples) soliton trains appear in the Bose-Fermi mixture.Comment: 4 pages, 4 figure

Stabilization of a (3+1)D soliton in a Kerr medium by a rapidly oscillating dispersion coefficient

Using the numerical solution of the nonlinear Schroedinger equation and a variational method it is shown that (3+1)-dimensional spatiotemporal optical solitons can be stabilized by a rapidly oscillating dispersion coefficient in a Kerr medium with cubic nonlinearity. This has immediate consequence in generating dispersion-managed robust optical soliton in communication as well as possible stabilized Bose-Einstein condensates in periodic optical-lattice potential via an effective-mass formulation. We also critically compare the present stabilization with that obtained by a rapid sinusoidal oscillation of the Kerr nonlinearity parameter.Comment: 6 pages, 6 ps figures, New figure 4 added, Physical Review

Combination of inverse spectral transform method and method of characteristics: deformed Pohlmeyer equation

We apply a version of the dressing method to a system of four dimensional nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform Method) and nonlinear matrix PDE integrable by the method of characteristics as particular reductions. Some other reductions are suggested.Comment: 12 page

Variation of jet quenching from RHIC to LHC and thermal suppression of QCD coupling constant

We perform a joint jet tomographic analysis of the data on the nuclear modification factor $R_{AA}$ from PHENIX at RHIC and ALICE at LHC. The computations are performed accounting for radiative and collisional parton energy loss with running coupling constant. Our results show that the observed slow variation of $R_{AA}$ from RHIC to LHC indicates that the QCD coupling constant is suppressed in the quark-gluon plasma produced at LHC.Comment: 9 pages, 2 figure

Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies

Analytic-bilinear approach for construction and study of integrable hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice hierarchies are considered. This approach allows to represent generalized hierarchies of integrable equations in a condensed form of finite functional equations. Generalized hierarchy incorporates basic hierarchy, modified hierarchy, singularity manifold equation hierarchy and corresponding linear problems. Different levels of generalized hierarchy are connected via invariants of Combescure symmetry transformation. Resolution of functional equations also leads to the $\tau$-function and addition formulae to it.Comment: 43 pages, Late

Instability and Evolution of Nonlinearly Interacting Water Waves

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term evolution of the latter by means of computer simulations of the governing nonlinear equations and demonstrate the formation of localized coherent wave envelopes. Our results should be useful for understanding the formation and nonlinear propagation characteristics of large amplitude freak waves in deep water.Comment: 4 pages, 4 figures, to appear in Physical Review Letter

Solitary waves and yrast states in Bose-Einstein condensed gases of atoms

Considering a Bose-Einstein condensed gas confined in one dimension with periodic boundary conditions, we demonstrate that, very generally, solitary-wave and rotational excitations coincide. This exact equivalence allows us to establish connections between a number of effects that are present in these two problems, many of which have been studied using the mean-field approximation.Comment: Revised version, where the generality of our arguments is presented more clearl

Energy loss in perturbative QCD

We review the properties of energetic parton propagation in hot or cold QCD matter, as obtained in recent works. Advances in understanding the energy loss - collisional and radiative - are summarized, with emphasis on the latter: it features very interesting properties which may help to detect the quark-gluon plasma produced in heavy ion collisions. We describe two different theoretical approaches, which lead to the same radiated gluon energy spectrum. The case of a longitudinally expanding QCD plasma is investigated. The energy lost by a jet with given opening angle is calculated in view of making predictions for the suppression (quenching) of hard jet production. Phenomenological implications for the difference between hot and cold matter are discussed. Numerical estimates of the loss suggest that it may be significantly enhanced in hot compared to cold matter.Comment: 49 pages latex file with 11 embedded PS figures. Uses ar.sty (included), one equation revised. submitted to Annual Review of Nuclear and Particle Scienc

Jet quenching with running coupling including radiative and collisional energy losses

We calculate the nuclear modification factor for RHIC and LHC conditions accounting for the radiative and collisional parton energy loss with the running coupling constant.We find that the RHIC data can be explained both in the scenario with the chemically equilibrium quark-gluon plasma and purely gluonic plasma with slightly different thermal suppression of the coupling constant. The role of the parton energy gain due to gluon absorption is also investigated. Our results show that the energy gain gives negligible effect.Comment: 11 pages, 3 figure

Stability of Bose-Einstein Condensates Confined in Traps

Bose-Einstein condensation has been realized in dilute atomic vapors. This achievement has generated immerse interest in this field. Presented is a review of recent theoretical research into the properties of trapped dilute-gas Bose-Einstein condensates. Among them, stability of Bose-Einstein condensates confined in traps is mainly discussed. Static properties of the ground state are investigated by use of the variational method. The anlysis is extended to the stability of two-component condensates. Time-development of the condensate is well-described by the Gross-Pitaevskii equation which is known in nonlinear physics as the nonlinear Schr\"odinger equation. For the case that the inter-atomic potential is effectively attractive, a singularity of the solution emerges in a finite time. This phenomenon which we call collapse explains the upper bound for the number of atoms in such condensates under traps.Comment: 74 pages with 12 figures, submitted to the review section of International Journal of Modern Physics