On Heavy-Quark Free Energies, Entropies, Polyakov Loop, and AdS/QCD

In this paper we explore some of the features of a heavy quark-antiquark pair at finite temperature using a five-dimensional framework nowadays known as AdS/QCD. We shall show that the resulting behavior is consistent with our qualitative expectations of thermal gauge theory. Some of the results are in good agreement with the lattice data that provides additional evidence for the validity of the proposed model.Comment: 15 pages, 10 figures; v2: comments added, misprints correcte

The Robinson-Trautman Type III Prolongation Structure Contains K2_2

The minimal prolongation structure for the Robinson-Trautman equations of Petrov type III is shown to always include the infinite-dimensional, contragredient algebra, K$_2$, which is of infinite growth. Knowledge of faithful representations of this algebra would allow the determination of B\"acklund transformations to evolve new solutions.Comment: 20 pages, plain TeX, no figures, submitted to Commun. Math. Phy

Stable two-dimensional solitary pulses in linearly coupled dissipative Kadomtsev-Petviashvili equations

A two-dimensional (2D) generalization of the stabilized Kuramoto - Sivashinsky (KS) system is presented. It is based on the Kadomtsev-Petviashvili (KP) equation including dissipation of the generic (Newell -- Whitehead -- Segel, NWS) type and gain. The system directly applies to the description of gravity-capillary waves on the surface of a liquid layer flowing down an inclined plane, with a surfactant diffusing along the layer's surface. Actually, the model is quite general, offering a simple way to stabilize nonlinear waves in media combining the weakly-2D dispersion of the KP type with gain and NWS dissipation. Parallel to this, another model is introduced, whose dissipative terms are isotropic, rather than of the NWS type. Both models include an additional linear equation of the advection-diffusion type, linearly coupled to the main KP-NWS equation. The extra equation provides for stability of the zero background in the system, opening a way to the existence of stable localized pulses. The consideration is focused on the case when the dispersive part of the system of the KP-I type, admitting the existence of 2D localized pulses. Treating the dissipation and gain as small perturbations and making use of the balance equation for the field momentum, we find that the equilibrium between the gain and losses may select two 2D solitons, from their continuous family existing in the conservative counterpart of the model (the latter family is found in an exact analytical form). The selected soliton with the larger amplitude is expected to be stable. Direct simulations completely corroborate the analytical predictions.Comment: a latex text file and 16 eps files with figures; Physical Review E, in pres

On universality of critical behavior in the focusing nonlinear Schr\uf6dinger equation, elliptic umbilic catastrophe and the Tritronqu\ue9e solution to the Painlev\ue9-I equation

We argue that the critical behavior near the point of "gradient catastrophe" of the solution to the Cauchy problem for the focusing nonlinear Schrodinger equation i epsilon Psi(t) + epsilon(2)/2 Psi(xx) + vertical bar Psi vertical bar(2)Psi = 0, epsilon << 1, with analytic initial data of the form Psi( x, 0; epsilon) = A(x)e(i/epsilon) (S(x)) is approximately described by a particular solution to the Painleve-I equation