The sDiff(2) Toda equation determines all self-dual, vacuum solutions of the Einstein field equations with one rotational Killing vector. Some history of the searches for non-trivial solutions is given, including those that begin with the limit as n → ∞ of the An Toda lattice equations. That approach is applied here to the known prolongation structure for the Toda lattice, hoping to use Bäcklun...

A sequence of solutions to the equation of symmetry for the continuous Toda chain in 1 + 2 dimensions is represented in explicit form. This fact leads to the supposition that this equation is completely integrable.

We numerically solve fully (3+1)-dimensional relativistic hydrodynamical equation coupled with the baryon number conservation law without spatial symmetry. We discuss the effect of transverse expansion based on the deviation our numerical result from Bjorken’s scaling solution. We analyze the space-time evolution of the QGP gas in the case of non cylindrical initial conditions.

We generalize the Toda lattice (or Toda chain) equation to the square lattice, i.e., we construct an integrable nonlinear equation for a scalar field taking values on the square lattice and depending on a continuous (time) variable, characterized by an exponential law of interaction in both discrete directions of the square lattice. We construct the Darboux-Bäcklund transformations for such lat...

We present the anyon equation on a cylinder and in an infinite potential wall from the abelian Chern-Simons theory coupled to non-relativistic matter field by obtaining the effective hamiltonian through the canonical transformation method used for the theory on a plane and on a torus. We also give the periodic property of the theory on the cylinder.

Using a formalism of minitwistors, we derive infinitely many conserved charges for the sl(∞)-Toda equation which accounts for gravitational instantons with a rotational Killing symmetry. These charges are shown to form an infinite dimensional algebra through the Poisson bracket which is isomorphic to two dimensional area preserving diffeomorphism with central extentions. E-mail address; be10@dk...

Starting from the presence of non-ideal plasma effects due to strongly coupled plasma in the early stage of relativistic heavy-ion collisions, we investigate, from a phenomenological point of view, the relevance of non-conventional statistical mechanics effects on the rapidity spectra of net proton yield at AGS, SPS and RHIC. We show that the broad rapidity shape measured at RHIC can be very we...

Currently there is not a satisfactory relativistic spontaneous collapse model. Here we show the impossibility of simple generalization continuous (CSL) model to framework. We consider mass coupled as in non-relativistic limit this gives CSL that Lorentz covariant equation cannot simultaneously satisfy following conditions: i) To avoid divergent rate energy, ii) prevent superluminal signaling.

A saddle point variational (SPV ) method was applied to the Dirac equation as an example of a fully relativistic equation with both negative and positive energy solutions. The effect of the negative energy states was mitigated by maximizing the energy with respect to a relevant parameter while at the same time minimizing it with respect to another parameter in the wave function. The Cornell pot...