Resonance and web structure in discrete soliton systems: the two-dimensional Toda lattice and its fully discrete and ultra-discrete versions Abstract. We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable s...

Starting from the presence of non-ideal plasma effects due to strong 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 well...

We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always pres...

Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description is reduced by use of the geometrical concept of the forms of rel-ativistic dynamics. The remainder gauge degrees of freedom of the electromagnetic potential...

The framework of point form relativistic quantum mechanics is used to construct interacting four-momentum operators in terms of creation and annihilation operators of underlying constituents. It is shown how to write the creation and annihilation operators in terms of discrete momenta, arising from discrete subgroups of the Lorentz group, in such a way that the Poincaré commutation relations ar...

The modular vector field plays an important role in the theory of Poisson manifolds and is intimately connected with the Poisson cohomology of the space. In this paper we investigate its significance in the theory of integrable systems. We illustrate in detail the case of the Toda lattice both in Flaschka and natural coordinates.

Given a classical r-matrix on a Poisson algebra, we show how to construct a natural family of compatible Poisson structures for the Hamiltonian formulation of Lax equations. Examples for which our formalism applies include the Benny hierachy, the dispersionless Toda lattice hierachy, the dispersionless KP and modified KP hierachies, the dispersionless Dym hierachy etc.

Studied is the Baxter equation for the quantum discrete Boussinesq equation. We explicitly construct the Baxter Q operator from a generating function of the local integrals of motion of the affine Toda lattice field theory, and show that it solves the third order operator-valued difference equation. nlin/0102021

Some techniques of bilinearization of the non-autonomous 1 + 1 dimensional discrete soliton equations is discussed by taking the discrete KdV equation, the discrete Toda lattice equation, and the discrete LotkaVolterra equation as examples. Casorati determinant solutions to those equations are also constructed explicitly.

The periodic Toda lattice with N sites is globally symplectomorphic to a two parameter family of N-1 coupled harmonic oscillators. The action variables fill out the whole positive quadrant of R(N-1). We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's theorem applies on (almost) al...